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Your Simple (Yes, Simple) Guide to Quantum Entanglement

An aura of glamorous mystery attaches to the concept of quantum entanglement , and also to the (somehow) related claim that quantum theory requires “many worlds.” Yet in the end those are, or should be, scientific ideas, with down-to-earth meanings and concrete implications. Here I’d like to explain the concepts of entanglement and many worlds as simply and clearly as I know how.

Entanglement is often regarded as a uniquely quantum-mechanical phenomenon, but it is not. In fact, it is enlightening, though somewhat unconventional, to consider a simple non-quantum (or “classical”) version of entanglement first. This enables us to pry the subtlety of entanglement itself apart from the general oddity of quantum theory.

Quanta Magazine

Original story reprinted with permission from Quanta Magazine , an editorially independent division of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences

Entanglement arises in situations where we have partial knowledge of the state of two systems. For example, our systems can be two objects that we’ll call c-ons. The “c” is meant to suggest “classical,” but if you’d prefer to have something specific and pleasant in mind, you can think of our c-ons as cakes.

Our c-ons come in two shapes, square or circular, which we identify as their possible states. Then the four possible joint states, for two c-ons, are (square, square), (square, circle), (circle, square), (circle, circle). The following tables show two examples of what the probabilities could be for finding the system in each of those four states.

We say that the c-ons are “independent” if knowledge of the state of one of them does not give useful information about the state of the other. Our first table has this property. If the first c-on (or cake) is square, we’re still in the dark about the shape of the second. Similarly, the shape of the second does not reveal anything useful about the shape of the first.

On the other hand, we say our two c-ons are entangled when information about one improves our knowledge of the other. Our second table demonstrates extreme entanglement. In that case, whenever the first c-on is circular, we know the second is circular too. And when the first c-on is square, so is the second. Knowing the shape of one, we can infer the shape of the other with certainty.

The quantum version of entanglement is essentially the same phenomenon—that is, lack of independence. In quantum theory, states are described by mathematical objects called wave functions. The rules connecting wave functions to physical probabilities introduce very interesting complications, as we will discuss, but the central concept of entangled knowledge, which we have seen already for classical probabilities, carries over.

Cakes don’t count as quantum systems, of course, but entanglement between quantum systems arises naturally—for example, in the aftermath of particle collisions. In practice, unentangled (independent) states are rare exceptions, for whenever systems interact, the interaction creates correlations between them.

Consider, for example, molecules. They are composites of subsystems, namely electrons and nuclei. A molecule’s lowest energy state, in which it is most usually found, is a highly entangled state of its electrons and nuclei, for the positions of those constituent particles are by no means independent. As the nuclei move, the electrons move with them.

Returning to our example: If we write Φ■, Φ● for the wave functions describing system 1 in its square or circular states, and ψ■, ψ● for the wave functions describing system 2 in its square or circular states, then in our working example the overall states will be

Independent: Φ■ ψ■ + Φ■ ψ● + Φ● ψ■ + Φ● ψ●

Entangled: Φ■ ψ■ + Φ● ψ●

We can also write the independent version as

(Φ■ + Φ●)(ψ■ + ψ●)

Note how in this formulation the parentheses clearly separate systems 1 and 2 into independent units.

There are many ways to create entangled states. One way is to make a measurement of your (composite) system that gives you partial information. We can learn, for example, that the two systems have conspired to have the same shape, without learning exactly what shape they have. This concept will become important later.

The more distinctive consequences of quantum entanglement, such as the Einstein-Podolsky-Rosen (EPR) and Greenberger-Horne-Zeilinger (GHZ) effects, arise through its interplay with another aspect of quantum theory called “complementarity.” To pave the way for discussion of EPR and GHZ, let me now introduce complementarity.

Previously, we imagined that our c-ons could exhibit two shapes (square and circle). Now we imagine that it can also exhibit two colors—red and blue. If we were speaking of classical systems, like cakes, this added property would imply that our c-ons could be in any of four possible states: a red square, a red circle, a blue square or a blue circle.

Yet for a quantum cake—a quake, perhaps, or (with more dignity) a q-on—the situation is profoundly different. The fact that a q-on can exhibit, in different situations, different shapes or different colors does not necessarily mean that it possesses both a shape and a color simultaneously. In fact, that “common sense” inference, which Einstein insisted should be part of any acceptable notion of physical reality, is inconsistent with experimental facts, as we’ll see shortly.

We can measure the shape of our q-on, but in doing so we lose all information about its color. Or we can measure the color of our q-on, but in doing so we lose all information about its shape. What we cannot do, according to quantum theory, is measure both its shape and its color simultaneously. No one view of physical reality captures all its aspects; one must take into account many different, mutually exclusive views, each offering valid but partial insight. This is the heart of complementarity, as Niels Bohr formulated it.

As a consequence, quantum theory forces us to be circumspect in assigning physical reality to individual properties. To avoid contradictions, we must admit that:

• A property that is not measured need not exist.
• Measurement is an active process that alters the system being measured.

Now I will describe two classic—though far from classical!—illustrations of quantum theory’s strangeness. Both have been checked in rigorous experiments. (In the actual experiments, people measure properties like the angular momentum of electrons rather than shapes or colors of cakes.)

Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) described a startling effect that can arise when two quantum systems are entangled. The EPR effect marries a specific, experimentally realizable form of quantum entanglement with complementarity.

An EPR pair consists of two q-ons, each of which can be measured either for its shape or for its color (but not for both). We assume that we have access to many such pairs, all identical, and that we can choose which measurements to make of their components. If we measure the shape of one member of an EPR pair, we find it is equally likely to be square or circular. If we measure the color, we find it is equally likely to be red or blue.

The interesting effects, which EPR considered paradoxical, arise when we make measurements of both members of the pair. When we measure both members for color, or both members for shape, we find that the results always agree. Thus if we find that one is red, and later measure the color of the other, we will discover that it too is red, and so forth. On the other hand, if we measure the shape of one, and then the color of the other, there is no correlation. Thus if the first is square, the second is equally likely to be red or to be blue.

We will, according to quantum theory, get those results even if great distances separate the two systems, and the measurements are performed nearly simultaneously. The choice of measurement in one location appears to be affecting the state of the system in the other location. This “spooky action at a distance,” as Einstein called it, might seem to require transmission of information — in this case, information about what measurement was performed — at a rate faster than the speed of light.

But does it? Until I know the result you obtained, I don’t know what to expect. I gain useful information when I learn the result you’ve measured, not at the moment you measure it. And any message revealing the result you measured must be transmitted in some concrete physical way, slower (presumably) than the speed of light.

Upon deeper reflection, the paradox dissolves further. Indeed, let us consider again the state of the second system, given that the first has been measured to be red. If we choose to measure the second q-on’s color, we will surely get red. But as we discussed earlier, when introducing complementarity, if we choose to measure a q-on’s shape, when it is in the “red” state, we will have equal probability to find a square or a circle. Thus, far from introducing a paradox, the EPR outcome is logically forced. It is, in essence, simply a repackaging of complementarity.

Nor is it paradoxical to find that distant events are correlated. After all, if I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine the handedness of the glove in the other. Similarly, in all known cases the correlations between an EPR pair must be imprinted when its members are close together, though of course they can survive subsequent separation, as though they had memories. Again, the peculiarity of EPR is not correlation as such, but its possible embodiment in complementary forms.

Daniel Greenberger , Michael Horne and Anton Zeilinger discovered another brilliantly illuminating example of quantum entanglement . It involves three of our q-ons, prepared in a special, entangled state (the GHZ state). We distribute the three q-ons to three distant experimenters. Each experimenter chooses, independently and at random, whether to measure shape or color, and records the result. The experiment gets repeated many times, always with the three q-ons starting out in the GHZ state.

Each experimenter, separately, finds maximally random results. When she measures a q-on’s shape, she is equally likely to find a square or a circle; when she measures its color, red or blue are equally likely. So far, so mundane.

But later, when the experimenters come together and compare their measurements, a bit of analysis reveals a stunning result. Let us call square shapes and red colors “good,” and circular shapes and blue colors “evil.” The experimenters discover that whenever two of them chose to measure shape but the third measured color, they found that exactly 0 or 2 results were “evil” (that is, circular or blue). But when all three chose to measure color, they found that exactly 1 or 3 measurements were evil. That is what quantum mechanics predicts, and that is what is observed.

So: Is the quantity of evil even or odd? Both possibilities are realized, with certainty, in different sorts of measurements. We are forced to reject the question. It makes no sense to speak of the quantity of evil in our system, independent of how it is measured. Indeed, it leads to contradictions.

The GHZ effect is, in the physicist Sidney Coleman’s words, “quantum mechanics in your face.” It demolishes a deeply embedded prejudice, rooted in everyday experience, that physical systems have definite properties, independent of whether those properties are measured. For if they did, then the balance between good and evil would be unaffected by measurement choices. Once internalized, the message of the GHZ effect is unforgettable and mind-expanding.

Thus far we have considered how entanglement can make it impossible to assign unique, independent states to several q-ons. Similar considerations apply to the evolution of a single q-on in time.

We say we have “entangled histories” when it is impossible to assign a definite state to our system at each moment in time . Similarly to how we got conventional entanglement by eliminating some possibilities, we can create entangled histories by making measurements that gather partial information about what happened. In the simplest entangled histories, we have just one q-on, which we monitor at two different times. We can imagine situations where we determine that the shape of our q-on was either square at both times or that it was circular at both times, but that our observations leave both alternatives in play. This is a quantum temporal analogue of the simplest entanglement situations illustrated above.

Using a slightly more elaborate protocol we can add the wrinkle of complementarity to this system, and define situations that bring out the “many worlds” aspect of quantum theory. Thus our q-on might be prepared in the red state at an earlier time, and measured to be in the blue state at a subsequent time. As in the simple examples above, we cannot consistently assign our q-on the property of color at intermediate times; nor does it have a determinate shape. Histories of this sort realize, in a limited but controlled and precise way, the intuition that underlies the many worlds picture of quantum mechanics. A definite state can branch into mutually contradictory historical trajectories that later come together.

Erwin Schrödinger, a founder of quantum theory who was deeply skeptical of its correctness, emphasized that the evolution of quantum systems naturally leads to states that might be measured to have grossly different properties. His “Schrödinger cat” states, famously, scale up quantum uncertainty into questions about feline mortality. Prior to measurement, as we’ve seen in our examples, one cannot assign the property of life (or death) to the cat. Both—or neither—coexist within a netherworld of possibility.

Everyday language is ill suited to describe quantum complementarity, in part because everyday experience does not encounter it. Practical cats interact with surrounding air molecules, among other things, in very different ways depending on whether they are alive or dead, so in practice the measurement gets made automatically, and the cat gets on with its life (or death). But entangled histories describe q-ons that are, in a real sense, Schrödinger kittens. Their full description requires, at intermediate times, that we take both of two contradictory property-trajectories into account.

The controlled experimental realization of entangled histories is delicate because it requires we gather partial information about our q-on. Conventional quantum measurements generally gather complete information at one time—for example, they determine a definite shape, or a definite color—rather than partial information spanning several times. But it can be done—indeed, without great technical difficulty. In this way we can give definite mathematical and experimental meaning to the proliferation of “many worlds” in quantum theory, and demonstrate its substantiality.

Original story reprinted with permission from Quanta Magazine , an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

What Is Entanglement and Why Is It Important?

Entanglement is at the heart of quantum physics and future quantum technologies. Like other aspects of quantum science, the phenomenon of entanglement reveals itself at very tiny, subatomic scales. When two particles, such as a pair of photons or electrons, become entangled, they remain connected even when separated by vast distances. In the same way that a ballet or tango emerges from individual dancers, entanglement arises from the connection between particles. It is what scientists call an emergent property.

How do scientists explain quantum entanglement?

In the video below, Caltech faculty members take a stab at explaining entanglement. Featured: Rana Adhikari, professor of physics; Xie Chen, professor of theoretical physics; Manuel Endres, professor of physics and Rosenberg Scholar; and John Preskill, Richard P. Feynman Professor of Theoretical Physics, Allen V. C. Davis and Lenabelle Davis Leadership Chair, and director of the Institute for Quantum Information and Matter.

Unbreakable Correlation

When researchers study entanglement , they often use a special kind of crystal to generate two entangled particles from one. The entangled particles are then sent off to different locations. For this example, let's say the researchers want to measure the direction the particles are spinning, which can be either up or down along a given axis. Before the particles are measured, each will be in a state of superposition , or both "spin up" and "spin down" at the same time.

If the researcher measures the direction of one particle's spin and then repeats the measurement on its distant, entangled partner, that researcher will always find that the pair are correlated: if one particle's spin is up, the other's will be down (the spins may instead both be up or both be down, depending on how the experiment is designed, but there will always be a correlation). Returning to our dancer metaphor, this would be like observing one dancer and finding them in a pirouette, and then automatically knowing the other dancer must also be performing a pirouette. The beauty of entanglement is that just knowing the state of one particle automatically tells you something about its companion, even when they are far apart.

Are particles really connected across space?

But are the particles really somehow tethered to each other across space, or is something else going on? Some scientists, including Albert Einstein in the 1930s, pointed out that the entangled particles might have always been spin up or spin down, but that this information was hidden from us until the measurements were made. Such "local hidden variable theories" argued against the mind-boggling aspect of entanglement, instead proposing that something more mundane, yet unseen, is going on.

Thanks to theoretical work by John Stewart Bell in the 1960s, and experimental work done by Caltech alumnus John Clauser (BS '64) and others beginning in the 1970s, scientists have ruled out these local hidden-variable theories. A key to the researchers' success involved observing entangled particles from different angles. In the experiment mentioned above, this means that a researcher would measure their first particle as spin up, but then use a different viewing angle (or a different spin axis direction) to measure the second particle. Rather than the two particles matching up as before, the second particle would have gone back into a state of superposition and, once observed, could be either spin up or down. The choice of the viewing angle changed the outcome of the experiment, which means that there cannot be any hidden information buried inside a particle that determines its spin before it is observed. The dance of entanglement materializes not from any one particle but from the connections between them.

Relativity Remains Intact

A common misconception about entanglement is that the particles are communicating with each other faster than the speed of light, which would go against Einstein's special theory of relativity. Experiments have shown that this is not true, nor can quantum physics be used to send faster-than-light communications. Though scientists still debate how the seemingly bizarre phenomenon of entanglement arises, they know it is a real principle that passes test after test. In fact, while Einstein famously described entanglement as "spooky action at a distance," today's quantum scientists say there is nothing spooky about it.

"It may be tempting to think that the particles are somehow communicating with each other across these great distances, but that is not the case," says Thomas Vidick , a professor of computing and mathematical sciences at Caltech. "There can be correlation without communication," and the particles "can be thought of as one object."

Networks of Entanglement

Entanglement can also occur among hundreds, millions, and even more particles. The phenomenon is thought to take place throughout nature, among the atoms and molecules in living species and within metals and other materials. When hundreds of particles become entangled, they still act as one unified object. Like a flock of birds, the particles become a whole entity unto itself without being in direct contact with one another. Caltech scientists focus on the study of these so-called many-body entangled systems, both to understand the fundamental physics and to create and develop new quantum technologies. As John Preskill, Caltech's Richard P. Feynman Professor of Theoretical Physics, Allen V. C. Davis and Lenabelle Davis Leadership Chair, and director of the Institute for Quantum Information and Matter, says, "We are making investments in and betting on entanglement being one of the most important themes of 21st-century science."

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Nobel Prize : Quantum Entanglement Unveiled

7 October 2022: We have replaced our initial one-paragraph announcement with a full-length Focus story.

The Nobel Prize in Physics this year recognizes efforts to take quantum weirdness out of philosophy discussions and to place it on experimental display for all to see. The award is shared by Alain Aspect, John Clauser, and Anton Zeilinger, all of whom showed a mastery of entanglement—a quantum relationship between two particles that can exist over long distances. Using entangled photons, Clauser and Aspect performed some of the first “Bell tests,” which confirmed quantum mechanics predictions while putting to bed certain alternative theories based on classical physics. Zeilinger used some of those Bell-test techniques to demonstrate entanglement control methods that can be applied to quantum computing, quantum cryptography, and other quantum information technologies.

Since its inception, quantum mechanics has been wildly successful at predicting the outcomes of experiments. But the theory assumes that some properties of a particle are inherently uncertain—a fact that bothered many physicists, including Albert Einstein. He and his colleagues expressed their concern in a paradox they described in 1935 [ 1 ]: Imagine creating two quantum mechanically entangled particles and distributing them between two separated researchers, characters later named Alice and Bob. If Alice measures her particle, then she learns something about Bob’s particle—as if her measurement instantaneously changed the uncertainty about the state of his particle. To avoid such “spooky action at a distance,” Einstein proposed that lying underneath the quantum framework is a set of classical “hidden variables” that determine precisely how a particle will behave, rather than providing only probabilities.

The hidden variables were unmeasurable—by definition—so most physicists deemed their existence to be a philosophical issue, not an experimental one. That changed in 1964 when John Bell of the University of Wisconsin-Madison, proposed a thought experiment that could directly test the hidden variable hypothesis [ 2 ]. As in Einstein’s paradox, Alice and Bob are each sent one particle of an entangled pair. This time, however, the two researchers measure their respective particles in different ways and compare their results. Bell showed that if hidden variables exist, the experimental results would obey a mathematical inequality. However, if quantum mechanics was correct, the inequality would be violated.

Bell’s work showed how to settle the debate between quantum and classical views, but his proposed experiment assumed detector capabilities that weren’t feasible. A revised version using photons and polarizers was proposed in 1969 by Clauser, then at Columbia University, along with his colleagues [ 3 ]. Three years later, Clauser and Stuart Freedman (both at the University of California, Berkeley) succeeded in performing that experiment [ 4 ].

The Freedman-Clauser experiment used entangled photons obtained by exciting calcium atoms. When a calcium atom de-excites, it can emit two photons whose polarizations are aligned. The researchers installed two detectors (Alice and Bob) on opposite sides of the calcium source and measured the rate of coincidences—two photons hitting the detectors simultaneously. Each detector was equipped with a polarizer that could be rotated to an arbitrary orientation.

Freedman and Clauser showed theoretically that quantum mechanics predictions diverge strongly from hidden variable predictions when Alice and Bob’s polarizers are offset from each other by 22.5° or 67.5°. The researchers collected 200 hours of data and found that the coincidence rates violated a revamped Bell’s inequality, proving that quantum mechanics is right.

The results of the first Bell test were a blow to hidden variables, but there were “loopholes” that hidden-variable supporters could claim to rescue their theory. One of the most significant loopholes was based on the idea that the setting of Alice’s polarizer could have some influence on Bob’s polarizer or on the photons that are created at the source. Such effects could allow the elements of a hidden-variable system to “conspire” together to produce measurement outcomes that mimic quantum mechanics.

To close this so-called locality loophole, Aspect and his colleagues at the Institute of Optics Graduate School in France performed an updated Bell test in 1982, using an innovative method for randomly changing the polarizer orientations [ 5 ]. The system worked like a railroad switch, rapidly diverting photons between two separate “tracks,” each with a different polarizer. The changes were made as the photons were traveling from the source to the detectors, so there was not enough time for coordination between supposed hidden variables.

Zeilinger, who is now at the University of Vienna, has also worked on removing loopholes from Bell tests (see Viewpoint: Closing the Door on Einstein and Bohr’s Quantum Debate , written by Aspect). In 2017, for example, he and his collaborators devised a way to use light from distant stars as a random input for setting polarizer orientations (see Synopsis: Cosmic Test of Quantum Mechanics ).

Zeilinger also used the techniques of entanglement control to explore practical applications, such as quantum teleportation and entanglement swapping. For the latter, he and his team showed in 1998 that they could create entanglement between two photons that were never in contact [ 6 ]. In this experiment, two sets of entangled photon pairs are generated at two separate locations. One from each pair is sent to Alice and Bob, while the other two photons are sent to a third person, Cecilia. Cecilia performs a Bell-like test on her two photons, and when she records a particular result, Alice’s photon winds up being entangled with Bob's. This swapping could be used to send entanglement over longer distances than is currently possible with optical fibers (see Research News: The Key Device Needed for a Quantum Internet ).

“Quantum entanglement is not questioned anymore,” says quantum physicist Jean Dalibard from the College of France. “It has become a tool, in particular in the emerging field of quantum information processing, and the three nominated scientists can be considered as the godfathers of this new domain.”

Quantum information specialist Jian-Wei Pan of the University of Science and Technology of China in Hefei says the winners are fully deserving of the prize. He has worked with Zeilinger on several projects, including a quantum-based satellite link (see Focus: Intercontinental, Quantum-Encrypted Messaging and Video ). “Now, in China, we are putting a lot of effort into actually turning these dreams into reality, hoping to make the quantum technologies practically useful for our society.”

–Michael Schirber

Michael Schirber is a Corresponding Editor for  Physics Magazine based in Lyon, France.

• A. Einstein et al. , “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47 , 777 (1935) .
• J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1 , 195 (1964) .
• J. F. Clauser et al. , “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23 , 880 (1969) .
• S. J. Freedman and J. F. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28 , 938 (1972) .
• A. Aspect et al. , “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49 , 1804 (1982) .
• J. W. Pan et al. , “Experimental entanglement swapping: Entangling photons that never interacted,” Phys. Rev. Lett. 80 , 3891 (1998) .

More Information

Research News: Hiding Secrets Using Quantum Entanglement

Research News: Diagramming Quantum Weirdness

APS press release

The Nobel Prize in Physics 2022 (Nobel Foundation)

Experimental Test of Bell's Inequalities Using Time-Varying Analyzers

Alain Aspect, Jean Dalibard, and Gérard Roger

Phys. Rev. Lett. 49 , 1804 (1982)

Published December 20, 1982

Experimental Entanglement Swapping: Entangling Photons That Never Interacted

Jian-Wei Pan, Dik Bouwmeester, Harald Weinfurter, and Anton Zeilinger

Phys. Rev. Lett. 80 , 3891 (1998)

Published May 4, 1998

Experimental Test of Local Hidden-Variable Theories

Stuart J. Freedman and John F. Clauser

Phys. Rev. Lett. 28 , 938 (1972)

Published April 3, 1972

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What is quantum entanglement? A physicist explains Einstein’s ‘spooky action at a distance’

The 2022 Nobel Prize in physics recognized three scientists who made groundbreaking contributions in understanding one of the most mysterious of all natural phenomena: quantum entanglement.

In the simplest terms, quantum entanglement means that aspects of one particle of an entangled pair depend on aspects of the other particle, no matter how far apart they are or what lies between them. These particles could be, for example, electrons or photons, and an aspect could be the state it is in, such as whether it is “spinning” in one direction or another.

The strange part of quantum entanglement is that when you measure something about one particle in an entangled pair, you immediately know something about the other particle, even if they are millions of light years apart. This odd connection between the two particles is instantaneous, seemingly breaking a fundamental law of the universe . Albert Einstein famously called the phenomenon “spooky action at a distance.”

Having spent the better part of two decades conducting experiments rooted in quantum mechanics , I have come to accept its strangeness. Thanks to ever more precise and reliable instruments and the work of this year’s Nobel winners, Alain Aspect , John Clauser and Anton Zeilinger , physicists now integrate quantum phenomena into their knowledge of the world with an exceptional degree of certainty.

However, even until the 1970s, researchers were still divided over whether quantum entanglement was a real phenomenon. And for good reasons – who would dare contradict the great Einstein, who himself doubted it? It took the development of new experimental technology and bold researchers to finally put this mystery to rest.

Existing in multiple states at once

To truly understand the spookiness of quantum entanglement, it is important to first understand quantum superposition . Quantum superposition is the idea that particles exist in multiple states at once. When a measurement is performed, it is as if the particle selects one of the states in the superposition.

For example, many particles have an attribute called spin that is measured either as “up” or “down” for a given orientation of the analyzer. But until you measure the spin of a particle, it simultaneously exists in a superposition of spin up and spin down.

There is a probability attached to each state, and it is possible to predict the average outcome from many measurements. The likelihood of a single measurement being up or down depends on these probabilities, but is itself unpredictable .

Though very weird, the mathematics and a vast number of experiments have shown that quantum mechanics correctly describes physical reality.

Two entangled particles

The spookiness of quantum entanglement emerges from the reality of quantum superposition, and was clear to the founding fathers of quantum mechanics who developed the theory in the 1920s and 1930s.

To create entangled particles you essentially break a system into two, where the sum of the parts is known. For example, you can split a particle with spin of zero into two particles that necessarily will have opposite spins so that their sum is zero.

In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published a paper that describes a thought experiment designed to illustrate a seeming absurdity of quantum entanglement that challenged a foundational law of the universe.

A simplified version of this thought experiment , attributed to David Bohm, considers the decay of a particle called the pi meson. When this particle decays, it produces an electron and a positron that have opposite spin and are moving away from each other. Therefore, if the electron spin is measured to be up, then the measured spin of the positron could only be down, and vice versa. This is true even if the particles are billions of miles apart.

This would be fine if the measurement of the electron spin were always up and the measured spin of the positron were always down. But because of quantum mechanics, the spin of each particle is both part up and part down until it is measured. Only when the measurement occurs does the quantum state of the spin “collapse” into either up or down – instantaneously collapsing the other particle into the opposite spin. This seems to suggest that the particles communicate with each other through some means that moves faster than the speed of light. But according to the laws of physics, nothing can travel faster than the speed of light. Surely the measured state of one particle cannot instantaneously determine the state of another particle at the far end of the universe?

Physicists, including Einstein, proposed a number of alternative interpretations of quantum entanglement in the 1930s. They theorized there was some unknown property – dubbed hidden variables – that determined the state of a particle before measurement . But at the time, physicists did not have the technology nor a definition of a clear measurement that could test whether quantum theory needed to be modified to include hidden variables.

Disproving a theory

It took until the 1960s before there were any clues to an answer. John Bell, a brilliant Irish physicist who did not live to receive the Nobel Prize, devised a scheme to test whether the notion of hidden variables made sense.

Bell produced an equation now known as Bell’s inequality that is always correct – and only correct – for hidden variable theories, and not always for quantum mechanics. Thus, if Bell’s equation was found not to be satisfied in a real-world experiment, local hidden variable theories can be ruled out as an explanation for quantum entanglement.

The experiments of the 2022 Nobel laureates, particularly those of Alain Aspect , were the first tests of the Bell inequality . The experiments used entangled photons, rather than pairs of an electron and a positron, as in many thought experiments. The results conclusively ruled out the existence of hidden variables, a mysterious attribute that would predetermine the states of entangled particles. Collectively, these and many follow-up experiments have vindicated quantum mechanics. Objects can be correlated over large distances in ways that physics before quantum mechanics can not explain.

Importantly, there is also no conflict with special relativity, which forbids faster-than-light communication . The fact that measurements over vast distances are correlated does not imply that information is transmitted between the particles. Two parties far apart performing measurements on entangled particles cannot use the phenomenon to pass along information faster than the speed of light.

Today, physicists continue to research quantum entanglement and investigate potential practical applications . Although quantum mechanics can predict the probability of a measurement with incredible accuracy, many researchers remain skeptical that it provides a complete description of reality. One thing is certain, though. Much remains to be said about the mysterious world of quantum mechanics.

Andreas Muller , Associate Professor of Physics, University of South Florida

This article is republished from The Conversation under a Creative Commons license. Read the original article .

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Associate Professor of Physics, University of South Florida

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The 2022 Nobel Prize in physics recognized three scientists who made groundbreaking contributions in understanding one of the most mysterious of all natural phenomena: quantum entanglement.

In the simplest terms, quantum entanglement means that aspects of one particle of an entangled pair depend on aspects of the other particle, no matter how far apart they are or what lies between them. These particles could be, for example, electrons or photons, and an aspect could be the state it is in, such as whether it is “spinning” in one direction or another.

The strange part of quantum entanglement is that when you measure something about one particle in an entangled pair, you immediately know something about the other particle, even if they are millions of light years apart. This odd connection between the two particles is instantaneous, seemingly breaking a fundamental law of the universe . Albert Einstein famously called the phenomenon “spooky action at a distance.”

Having spent the better part of two decades conducting experiments rooted in quantum mechanics , I have come to accept its strangeness. Thanks to ever more precise and reliable instruments and the work of this year’s Nobel winners, Alain Aspect , John Clauser and Anton Zeilinger , physicists now integrate quantum phenomena into their knowledge of the world with an exceptional degree of certainty.

However, even until the 1970s, researchers were still divided over whether quantum entanglement was a real phenomenon. And for good reasons – who would dare contradict the great Einstein, who himself doubted it? It took the development of new experimental technology and bold researchers to finally put this mystery to rest.

Existing in multiple states at once

To truly understand the spookiness of quantum entanglement, it is important to first understand quantum superposition . Quantum superposition is the idea that particles exist in multiple states at once. When a measurement is performed, it is as if the particle selects one of the states in the superposition.

For example, many particles have an attribute called spin that is measured either as “up” or “down” for a given orientation of the analyzer. But until you measure the spin of a particle, it simultaneously exists in a superposition of spin up and spin down.

There is a probability attached to each state, and it is possible to predict the average outcome from many measurements. The likelihood of a single measurement being up or down depends on these probabilities, but is itself unpredictable .

Though very weird, the mathematics and a vast number of experiments have shown that quantum mechanics correctly describes physical reality.

Two entangled particles

The spookiness of quantum entanglement emerges from the reality of quantum superposition, and was clear to the founding fathers of quantum mechanics who developed the theory in the 1920s and 1930s.

To create entangled particles you essentially break a system into two, where the sum of the parts is known. For example, you can split a particle with spin of zero into two particles that necessarily will have opposite spins so that their sum is zero.

In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published a paper that describes a thought experiment designed to illustrate a seeming absurdity of quantum entanglement that challenged a foundational law of the universe.

A simplified version of this thought experiment , attributed to David Bohm, considers the decay of a particle called the pi meson. When this particle decays, it produces an electron and a positron that have opposite spin and are moving away from each other. Therefore, if the electron spin is measured to be up, then the measured spin of the positron could only be down, and vice versa. This is true even if the particles are billions of miles apart.

This would be fine if the measurement of the electron spin were always up and the measured spin of the positron were always down. But because of quantum mechanics, the spin of each particle is both part up and part down until it is measured. Only when the measurement occurs does the quantum state of the spin “collapse” into either up or down – instantaneously collapsing the other particle into the opposite spin. This seems to suggest that the particles communicate with each other through some means that moves faster than the speed of light. But according to the laws of physics, nothing can travel faster than the speed of light. Surely the measured state of one particle cannot instantaneously determine the state of another particle at the far end of the universe?

Physicists, including Einstein, proposed a number of alternative interpretations of quantum entanglement in the 1930s. They theorized there was some unknown property – dubbed hidden variables – that determined the state of a particle before measurement . But at the time, physicists did not have the technology nor a definition of a clear measurement that could test whether quantum theory needed to be modified to include hidden variables.

Disproving a theory

It took until the 1960s before there were any clues to an answer. John Bell, a brilliant Irish physicist who did not live to receive the Nobel Prize, devised a scheme to test whether the notion of hidden variables made sense.

Bell produced an equation now known as Bell’s inequality that is always correct – and only correct – for hidden variable theories, and not always for quantum mechanics. Thus, if Bell’s equation was found not to be satisfied in a real-world experiment, local hidden variable theories can be ruled out as an explanation for quantum entanglement.

The experiments of the 2022 Nobel laureates, particularly those of Alain Aspect , were the first tests of the Bell inequality . The experiments used entangled photons, rather than pairs of an electron and a positron, as in many thought experiments. The results conclusively ruled out the existence of hidden variables, a mysterious attribute that would predetermine the states of entangled particles. Collectively, these and many follow-up experiments have vindicated quantum mechanics. Objects can be correlated over large distances in ways that physics before quantum mechanics can not explain.

Importantly, there is also no conflict with special relativity, which forbids faster-than-light communication . The fact that measurements over vast distances are correlated does not imply that information is transmitted between the particles. Two parties far apart performing measurements on entangled particles cannot use the phenomenon to pass along information faster than the speed of light.

Today, physicists continue to research quantum entanglement and investigate potential practical applications . Although quantum mechanics can predict the probability of a measurement with incredible accuracy, many researchers remain skeptical that it provides a complete description of reality. One thing is certain, though. Much remains to be said about the mysterious world of quantum mechanics.

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Quantum physics i, lecture 24: entanglement: qcomputing, epr, and bell's theorem.

Description: In this lecture, Prof. Adams discusses the basic principles of quantum computing. No-cloning theorem and Deutsch-Jozsa algorithm are introduced. The last part of the lecture is devoted to the EPR experiment and Bell’s inequality.

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How do you create quantum entanglement.

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One morning last week, I arrived on campus at the same time as a colleague from the History department who studies the history of physics. As we were walking toward the center of campus from the parking lot, he asked the title question of this post: "How do you create quantum entanglement?" He noted that he'd read a lot of pop-science articles talking about the weird aspects of the physics that happens once you have two entangled particles, but they tended to skip lightly over the details of how you get them entangled in the first place.

We had a nice conversation about it as we walked, and I filed that away as a topic for a blog post. I figured if my colleague was confused about that, then a bunch of other people probably are, too. And while I have certainly written a lot about entanglement here (The first page of Google results for "orzel forbes entanglement" gives one , two , three , four , five , six , seven , eight , nine links, and that's not all of them), it's also true that I haven't gone into that much detail about the creation of entanglement. Which turns out to be easier than you might think from pop-physics treatments that emphasize its weirdness, and that's an excellent excuse for a blog post.

Before we do that, though, it's important to set the basic parameters of what we mean by "quantum entanglement." The central idea is very simple: You have two particles, each of which can be in one of two states, and put them in a state where their states are indeterminate, but correlated. If you measure them individually, you get a random distribution of "0" and "1" answers, but if you repeat the measurements many times for many identically prepared pairs, you find that the resulting lists of "0" and "1" measurements are identical. The state of one of the two particles depends on the state of the other, and that correlation will hold even when they're separated.

Now, here's a brief description of four ways you can take two objects and put them in this kind of entangled quantum state:

Schematic of the third Aspect experiment testing quantum non-locality. Entangled photons from the ... [+] source are sent to two fast switches, that direct them to polarizing detectors. The switches change settings very rapidly, effectively changing the detector settings for the experiment while the photons are in flight. (Figure by Chad Orzel)

1) Entanglement From Birth: The vast majority of quantum entanglement experiments to date use photons as the entangled particles, for the simple reason that it's really easy to entangle two photons. And most of the ways people have to entangle photons just give you an entangled state right from the get-go.

The historical way of doing this is to use a "cascade" transition, as was done by Alain Aspect and colleagues in a classic set of experiments back in the early 1980s, and by Freedman and Clauser somewhat earlier. In these experiments, they put a bunch of calcium atoms into a highly-excited energy level where the electron is forbidden to return to the ground state by emitting a single photon. Instead, they decay by emitting two photons, passing through an intermediate state with a short lifetime. The emission of one photon is followed within a few nanoseconds by the emission of the second, so if you see one, you know the other should be around somewhere. And while these photons are emitted in random directions, when it happens that they're emitted in opposite directions, then conservation of angular requires that their polarizations have to be correlated with each other: that is, they need to be in an entangled state.

Cascade sources work, but they're pretty slow because each atom shoots photons out in random directions, so getting two photons sent in the right directions to hit your detectors can take a while. The quantum-entanglement business was revolutionized by the development of "parametric downconversion" sources, which use non-linear optical crystals to convert single high-energy photons into pairs of photons with half the initial energy. A violet laser shining into one of these crystals (the most common material used is "beta barium borate" or "BBO") will produce a small number of pairs of near-infrared photons. There's still a bit of randomness to the process, but conservation of momentum requires that the pairs come out on opposite sides of a cone around the original laser beam, allowing you to put two detectors in exactly the right place to catch the photons. And with the proper arrangement of the crystal (actually two thin crystals stuck together in the right way), the polarizations of the two photons will be correlated in exactly the way you need to demonstrate entanglement.

These parametric downconversion sources get you a much higher count rate, allowing the experiments to achieve truly ridiculous levels of statistical significance. The basic system is also simple enough to be an undergraduate lab experiment; we've had several students in recent years do their senior theses on parametric downconversion (not with entanglement, yet, but I have some summer students lined up to work on that). These are also the key sources for experiments on quantum teleportation, and many quantum information experiments. If you read a news story whose headline makes reference to Einstein's derisive description of entanglement, "spooky interaction at a distance," there's probably about a 75% chance it describes experiments that use parametric downconversion in some way.

Image of a scheme for ion-trap quantum computing. From Monroe group at JQI: http://iontrap.umd.edu/

2) Second-Generation Entanglement. Photons are great for demonstrating entanglement and transmitting information, but the world isn't just photons, and they have some significant disadvantages. Chief among them that they're kind of hard to keep around, since by definition they're always moving somewhere at the speed of light. For a lot of purposes, it would be nicer to entangle material particles instead, because they're easier to hold on to for long periods of time.

One of the simplest ways to imagine doing this is to just take a pair of photons that are produced in an entangled state, and direct them at, say, a pair of atoms that can absorb the photons in question. The end state of the photon absorption will depend on the polarization of the photons, so since the polarizations are indeterminate-but-correlated, you will end up with two atoms whose states are indeterminate-but-correlated.

In practice, this is kind of tricky, since the sorts of entangled photons you can generate easily don't connect readily to atomic states that last a long time. If you're clever, though, you can find ways to do this kind of thing, and convert entanglement of photons into entanglement of the atoms that absorb those photons.

Apparatus for entangling separated ions, showing the two vacuum systems. (Photo from JQI)

3) Entanglement By Accident. This method is a clever trick that sort of turns the previous method inside-out. That is, it starts with a pair of atoms at different locations that emit photons. Bringing the photons together in the right way can entangle the states of the two photons, in a way that leads to entanglement of the original atoms.

I first learned about this in experiments by Chris Monroe's group at Maryland (link to a write-up on my other blog), where they used ytterbium ions held in separate ion traps. The ions were excited to a state from which they could decay in one of two ways, emitting a photon with one of two polarizations. They collect the emitted photons, and bring them together on a beamsplitter, with two photodetectors placed at the two outputs of the beamsplitter.

In this configuration, about 25% of the time they get two photons reaching the beamsplitter, they'll detect one photon at each output. From quantum optics, we know that when this happens the two photons had opposite polarizations, meaning that the two ions have ended up in two different states. But they have no way of knowing which ion emitted which photon. Thus, the two ions end up entangled: if you measure the individual states, you get random results, but if you compare the lists of results for each ion over many repetitions, you find that they're perfectly correlated.

This is inherently probabilistic, and the original experiments in 2009(-ish) were very slow. They've done some refinements of the basic scheme, but it's still not as convenient a source of entangled pairs as you get with parametric downconversion. It is, however, an exceptionally cool trick, because the two ions are never anywhere close to each other -- they're trapped in entirely separate vacuum chambers, on different parts of the laser table. The only thing that's brought together is the light they emitted, but that's enough to entangle the ions, with all the weird results that follow from that.

Schematic of the Rydberg blockade scheme. Left: two ground-state atoms don't affect each other, and ... [+] can be excited by a laser (green arrow). Middle: Once one atom is excited, it shifts the energy levels of the other, blocking the laser excitation. Right: The entangled state that results from putting the first atom in a superposition and then trying to excite the second. (Figure by Chad Orzel)

4) Entanglement By Interaction. The coolest bit of the previous method -- that the ions are always separated -- points toward the final method of generating entanglement, which is just to bring the two together and let them interact in such a way that the final states of the two particles depend on each other. That is, after all, the essential meaning of what an entangled state is.

There are a bunch of ways of doing this, mostly associated with different quantum computing schemes, but it might be easiest to picture using a "Rydberg blockade" scheme. The idea here is that if you have two ground-state atoms separated by a smallish distance, they don't affect each other, but if you excite those atoms to a very high-energy state (a "Rydberg state" in atomic physics jargon), they interact over longer ranges, and can thus shift each others' energy levels.

If you arrange things properly, exciting one atom to the Rydberg state will shift the energy levels of the other by enough that it can't be excited by the same laser. So, you use a laser pulse to put one in a superposition of the ground state and the Rydberg state, then try to excite the second atom, it ends up in a superposition that's perfectly anti-correlated with the first atom: the part of the first atom that's in the ground state is paired with the part of the second atom that's in the Rydberg level, and vice versa. In other words, the two atoms are now entangled.

This is a simple example of an interaction that leads to indeterminate-but-correlated final states, but it gets the key idea across. Any time you can bring two systems together in such a way that the final state of one particle depends on the input state of the other, you can make an entangled state by making that input state a quantum superposition. This will necessarily lead to a pair of particles each of which is in an indeterminate state, with any eventual measurements of those states being perfectly correlated (or anti-correlated). It's a powerful idea, and central to pretty much every quantum computing scheme.

It's worth noting, here, that all of these schemes have a common feature, namely that the entanglement is created in a local manner. That is, the schemes either involve entangled particles that are in the same place at some point (entangled photons come from the same atom or input photon, and the interacting atoms are necessarily close together), or they interact via something passing between them at no more than light speed (an entangled photon pair traveling out to separate atoms, or the photons from two ions traveling to a beamsplitter). This is a critical feature for keeping the weirdness of entanglement contained -- you can't just arbitrarily entangle two particles that have no common history, which rules out most attempts to justify paranormal phenomena by invoking quantum entanglement.

These methods for generating entanglement are very general, and there are numerous technical details of implementing them with specific systems that I'm skipping over. These should help get the general ideas across, though, so the next time you read a pop-science article about quantum entanglement, you'll have a better idea of just where that comes from.

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Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently — instead, a quantum state may be given for the system as a whole.

Measurements of physical properties such as position, momentum, spin, polarization, etc., performed on entangled particles are found to be appropriately correlated . For example, if a pair of particles is generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise; because of the nature of quantum measurement. However, this behavior gives rise to paradoxical effects: any measurement of a property of a particle can be seen as acting on that particle (e.g., by collapsing a number of superposed states); and in the case of entangled particles, such action must be on the entangled system as a whole. It thus appears that one particle of an entangled pair “knows” what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances.

An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents (e.g., individual particles). If entangled, one constituent cannot be fully described without considering the other(s). Note that the state of a composite system is always expressible as a sum , or superposition, of products of states of local constituents; it is entangled if this sum necessarily has more than one term.

Quantum systems can become entangled through various types of interactions. Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made.

As an example of entanglement: a subatomic particle decays into an entangled pair of other particles . The decay events obey the various conservation laws, and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process). For instance, a spin-zero particle could decay into a pair of spin-½ particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be spin up on some axis, the other (when measured on the same axis) is always found to be spin down. (This is called the spin anti-correlated case; and if the prior probabilities for measuring each spin are equal, the pair is said to be in the singlet state.)

Experiment Description

The experiment described in this post is the repetition of the famous experiment of Wu – Shaknov in which it will demonstrate the angular correlation of gamma photons emitted from the annihilation of the positron and subsequently scattered by a compton scatterer.

We have already described in the post on the annihilation of the positron that the two gamma photons of 511 keV, for the conservation of momentum, are emitted on the same line but in opposite directions. From theoretical considerations also it is known that they have spin phased out by π/2 . The two photons that result from the annihilation of the positron have all what is need in order to form a single quantum system, from which it follows that the two gamma photons are entangled one to another.

The following diagram represents the experiment setup. The Na22 source of gamma photons is placed in between two lead ingots, with a hole in the center to give rise to two collimated beams of gamma rays. The collimated beams hit two iron cylinders that act as compton scatterer . The SiPM detectors with LYSO scintillator crystal are placed laterally so as to capture the radiation scattered at around 90° angle . One detector is maintained in a fixed position, while the other is positioned parallel to the first and subsequently placed orthogonal . The two detectors are operated in coincidence mode to detect only the photon pairs generated by the same annihilation.

The two gamma photons produced from annihilation have spin phased out by π/2 and their state of entangled photons should ensure that this angular correlation manifests itself with different counting rates in relation to the relative position of the two detectors. In particular, you should have the greater count rate when the two detectors are positioned orthogonal and minimum when they are parallel, the ratio between the two counting rates should have a value equal to 2.

The same experiment has been carried out using a PSoC (programmable system on chip) instead of the bunch of components shown in the image above. The link to this newest post is the following :  PSoC Coincidence Detector – I I

Measurements Results

Geometrical data

Lead Bricks : 150x150x50 mm Hole : diameter 10 mm Iron scatterer : cylinder diameter 12 mm x 30 mm long Scintillation Crystal :  LYSO 4x4x20 mm Position of the crystal : touching the scatterer Distance of the crystal : around 10 mm down the scatterer front face Distance of the scatterer face between the source : 50 mm

False Coincidence likelyhood

If we assume that the coincidence circuit has a time resolution of τ, then the probability of accidental coincidence is: P = 2τC1C2 = 2 x 2,5 x 10-7 x C1 x C2 Τ = 250 nsec C1 = counting rate on crystal 1 C2 = counting rate on crystal 2

Without scatterer and tuning the threshold of discriminator around 100keV the following counting rates are obtained :

C1 = 96 CPS C2 = 97 CPS P = 2 x 2,5 x 10 -7 x 96 x 97 = 4,66 x 10 -3 s -1 or 0,280 CPM

Background Measurements Data

Time = 12 h = 720 min N pulses = 221 σ = √N = 14,9 σ² = N = 221 From these data we can calculate the following value of background rate : 0,31 ± 0,02 CPM

Parallel detector Measurements Data

Time = 20 h = 1200 min N pulses = 878 σ = √N = 29,63 σ² = N = 878 From these data we can calculate the following value of the rate : 0,732 ± 0,025 CPM (background not subtracted) Subtracting the background σ = 0,068 0,422 ±  0,068 CPM (background subtracted)

Orthogonal detector Measurements Data

Time = 24 h = 1440 min N pulses = 1435 σ = √N = 37,88 σ² = N = 1435 From these data we can calculate the following value of the rate : 0,997 ±  0,026 CPM (background not subtracted) Subtracting the background σ = 0,068 0,687 ± 0,068 CPM (background subtracted)

Detector ǁ = 0,422 ± 0,068 CPM Detector Ⱶ = 0,687 ± 0,068 CPM

Detector ⱶ / detector ǁ = 0,687 / 0,422 = 1,63.

These values are compatible with the theoretical predictions (and the experimental verification made, for example, in the experiment of Wu-Shaknov) establishing a greater counting rate in the case where the detectors are orthogonal. This is considered a confirmation that the emitted gamma photons are polarized at planes shifted by 90° phase. This result is compatible with the hypothesis that the two gamma photons are entangled.

Improvements

The electronic part has been greatly improved with SiPM preamplifier and with a PSOC chip which does the “coincidence job”. The image below shows the new setup. This posts explain this new setup :  PSoC Coincidence Detector – I  ,  PSoC Coincidence Detector – I I .

Acknowledgements and References

We thank AdvanSiD , especially Claudio and Alessandro , for providing the SiPM modules used in the experiments. We thank Professor  Clifford John Bland for suggestions, support, and computer simulations. Article in “Scientific American” with description of a similar experiment :  How to build your own quantum entanglement experiment .

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Gamma Spectroscopy with KC761B

Abstract: in this article, we continue the presentation of the new KC761B device. In the previous post, we described the apparatus in general terms. Now we mainly focus on the gamma spectrometer functionality.

An editorially independent publication supported by the Simons Foundation.

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Entanglement Made Simple

April 28, 2016

An aura of glamorous mystery attaches to the concept of quantum entanglement , and also to the (somehow) related claim that quantum theory requires “many worlds.” Yet in the end those are, or should be, scientific ideas, with down-to-earth meanings and concrete implications. Here I’d like to explain the concepts of entanglement and many worlds as simply and clearly as I know how.

Entanglement is often regarded as a uniquely quantum-mechanical phenomenon, but it is not. In fact, it is enlightening, though somewhat unconventional, to consider a simple non-quantum (or “classical”) version of entanglement first. This enables us to pry the subtlety of entanglement itself apart from the general oddity of quantum theory.

Quantized A monthly column in which top researchers explore the process of discovery. This month’s columnist, Frank Wilczek, is a Nobel Prize-winning physicist at the Massachusetts Institute of Technology.

Entanglement arises in situations where we have partial knowledge of the state of two systems. For example, our systems can be two objects that we’ll call c-ons. The “c” is meant to suggest “classical,” but if you’d prefer to have something specific and pleasant in mind, you can think of our c-ons as cakes.

Our c-ons come in two shapes, square or circular, which we identify as their possible states. Then the four possible joint states, for two c-ons, are (square, square), (square, circle), (circle, square), (circle, circle). The following tables show two examples of what the probabilities could be for finding the system in each of those four states.

We say that the c-ons are “independent” if knowledge of the state of one of them does not give useful information about the state of the other. Our first table has this property. If the first c-on (or cake) is square, we’re still in the dark about the shape of the second. Similarly, the shape of the second does not reveal anything useful about the shape of the first.

On the other hand, we say our two c-ons are entangled when information about one improves our knowledge of the other. Our second table demonstrates extreme entanglement. In that case, whenever the first c-on is circular, we know the second is circular too. And when the first c-on is square, so is the second. Knowing the shape of one, we can infer the shape of the other with certainty.

The quantum version of entanglement is essentially the same phenomenon — that is, lack of independence. In quantum theory, states are described by mathematical objects called wave functions. The rules connecting wave functions to physical probabilities introduce very interesting complications, as we will discuss, but the central concept of entangled knowledge, which we have seen already for classical probabilities, carries over.

Cakes don’t count as quantum systems, of course, but entanglement between quantum systems arises naturally — for example, in the aftermath of particle collisions. In practice, unentangled (independent) states are rare exceptions, for whenever systems interact, the interaction creates correlations between them.

Consider, for example, molecules. They are composites of subsystems, namely electrons and nuclei. A molecule’s lowest energy state, in which it is most usually found, is a highly entangled state of its electrons and nuclei, for the positions of those constituent particles are by no means independent. As the nuclei move, the electrons move with them.

Returning to our example: If we write Φ ■ , Φ ● for the wave functions describing system 1 in its square or circular states, and ψ ■ , ψ ● for the wave functions describing system 2 in its square or circular states, then in our working example the overall states will be

Independent: Φ ■ ψ ■ + Φ ■ ψ ● + Φ ● ψ ■ + Φ ● ψ ●

Entangled: Φ ■ ψ ■ + Φ ● ψ ●

We can also write the independent version as

(Φ ■ + Φ ● )(ψ ■ + ψ ● )

Note how in this formulation the parentheses clearly separate systems 1 and 2 into independent units.

There are many ways to create entangled states. One way is to make a measurement of your (composite) system that gives you partial information. We can learn, for example, that the two systems have conspired to have the same shape, without learning exactly what shape they have. This concept will become important later.

The more distinctive consequences of quantum entanglement, such as the Einstein-Podolsky-Rosen (EPR) and Greenberger-Horne-Zeilinger (GHZ) effects, arise through its interplay with another aspect of quantum theory called “complementarity.” To pave the way for discussion of EPR and GHZ, let me now introduce complementarity.

Previously, we imagined that our c-ons could exhibit two shapes (square and circle). Now we imagine that it can also exhibit two colors — red and blue. If we were speaking of classical systems, like cakes, this added property would imply that our c-ons could be in any of four possible states: a red square, a red circle, a blue square or a blue circle.

Yet for a quantum cake — a quake, perhaps, or (with more dignity) a q-on — the situation is profoundly different. The fact that a q-on can exhibit, in different situations, different shapes or different colors does not necessarily mean that it possesses both a shape and a color simultaneously. In fact, that “common sense” inference, which Einstein insisted should be part of any acceptable notion of physical reality, is inconsistent with experimental facts, as we’ll see shortly.

We can measure the shape of our q-on, but in doing so we lose all information about its color. Or we can measure the color of our q-on, but in doing so we lose all information about its shape. What we cannot do, according to quantum theory, is measure both its shape and its color simultaneously. No one view of physical reality captures all its aspects; one must take into account many different, mutually exclusive views, each offering valid but partial insight. This is the heart of complementarity, as Niels Bohr formulated it.

As a consequence, quantum theory forces us to be circumspect in assigning physical reality to individual properties. To avoid contradictions, we must admit that:

• A property that is not measured need not exist.
• Measurement is an active process that alters the system being measured.

Now I will describe two classic — though far from classical! — illustrations of quantum theory’s strangeness. Both have been checked in rigorous experiments. (In the actual experiments, people measure properties like the angular momentum of electrons rather than shapes or colors of cakes.)

Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) described a startling effect that can arise when two quantum systems are entangled. The EPR effect marries a specific, experimentally realizable form of quantum entanglement with complementarity.

An EPR pair consists of two q-ons, each of which can be measured either for its shape or for its color (but not for both). We assume that we have access to many such pairs, all identical, and that we can choose which measurements to make of their components. If we measure the shape of one member of an EPR pair, we find it is equally likely to be square or circular. If we measure the color, we find it is equally likely to be red or blue.

The interesting effects, which EPR considered paradoxical, arise when we make measurements of both members of the pair. When we measure both members for color, or both members for shape, we find that the results always agree. Thus if we find that one is red, and later measure the color of the other, we will discover that it too is red, and so forth. On the other hand, if we measure the shape of one, and then the color of the other, there is no correlation. Thus if the first is square, the second is equally likely to be red or to be blue.

We will, according to quantum theory, get those results even if great distances separate the two systems, and the measurements are performed nearly simultaneously. The choice of measurement in one location appears to be affecting the state of the system in the other location. This “spooky action at a distance,” as Einstein called it, might seem to require transmission of information — in this case, information about what measurement was performed — at a rate faster than the speed of light.

But does it? Until I know the result you obtained, I don’t know what to expect. I gain useful information when I learn the result you’ve measured, not at the moment you measure it. And any message revealing the result you measured must be transmitted in some concrete physical way, slower (presumably) than the speed of light.

Upon deeper reflection, the paradox dissolves further. Indeed, let us consider again the state of the second system, given that the first has been measured to be red. If we choose to measure the second q-on’s color, we will surely get red. But as we discussed earlier, when introducing complementarity, if we choose to measure a q-on’s shape, when it is in the “red” state, we will have equal probability to find a square or a circle. Thus, far from introducing a paradox, the EPR outcome is logically forced. It is, in essence, simply a repackaging of complementarity.

Nor is it paradoxical to find that distant events are correlated. After all, if I put each member of a pair of gloves in boxes, and mail them to opposite sides of the earth, I should not be surprised that by looking inside one box I can determine the handedness of the glove in the other. Similarly, in all known cases the correlations between an EPR pair must be imprinted when its members are close together, though of course they can survive subsequent separation, as though they had memories. Again, the peculiarity of EPR is not correlation as such, but its possible embodiment in complementary forms.

Daniel Greenberger , Michael Horne and Anton Zeilinger discovered another brilliantly illuminating example of quantum entanglement . It involves three of our q-ons, prepared in a special, entangled state (the GHZ state). We distribute the three q-ons to three distant experimenters. Each experimenter chooses, independently and at random, whether to measure shape or color, and records the result. The experiment gets repeated many times, always with the three q-ons starting out in the GHZ state.

Each experimenter, separately, finds maximally random results. When she measures a q-on’s shape, she is equally likely to find a square or a circle; when she measures its color, red or blue are equally likely. So far, so mundane.

But later, when the experimenters come together and compare their measurements, a bit of analysis reveals a stunning result. Let us call square shapes and red colors “good,” and circular shapes and blue colors “evil.” The experimenters discover that whenever two of them chose to measure shape but the third measured color, they found that exactly 0 or 2 results were “evil” (that is, circular or blue). But when all three chose to measure color, they found that exactly 1 or 3 measurements were evil. That is what quantum mechanics predicts, and that is what is observed.

So: Is the quantity of evil even or odd? Both possibilities are realized, with certainty, in different sorts of measurements. We are forced to reject the question. It makes no sense to speak of the quantity of evil in our system, independent of how it is measured. Indeed, it leads to contradictions.

The GHZ effect is, in the physicist Sidney Coleman’s words, “quantum mechanics in your face.” It demolishes a deeply embedded prejudice, rooted in everyday experience, that physical systems have definite properties, independent of whether those properties are measured. For if they did, then the balance between good and evil would be unaffected by measurement choices. Once internalized, the message of the GHZ effect is unforgettable and mind-expanding.

Thus far we have considered how entanglement can make it impossible to assign unique, independent states to several q-ons. Similar considerations apply to the evolution of a single q-on in time.

We say we have “entangled histories” when it is impossible to assign a definite state to our system at each moment in time . Similarly to how we got conventional entanglement by eliminating some possibilities, we can create entangled histories by making measurements that gather partial information about what happened. In the simplest entangled histories, we have just one q-on, which we monitor at two different times. We can imagine situations where we determine that the shape of our q-on was either square at both times or that it was circular at both times, but that our observations leave both alternatives in play. This is a quantum temporal analogue of the simplest entanglement situations illustrated above.

Using a slightly more elaborate protocol we can add the wrinkle of complementarity to this system, and define situations that bring out the “many worlds” aspect of quantum theory. Thus our q-on might be prepared in the red state at an earlier time, and measured to be in the blue state at a subsequent time. As in the simple examples above, we cannot consistently assign our q-on the property of color at intermediate times; nor does it have a determinate shape. Histories of this sort realize, in a limited but controlled and precise way, the intuition that underlies the many worlds picture of quantum mechanics. A definite state can branch into mutually contradictory historical trajectories that later come together.

Erwin Schrödinger, a founder of quantum theory who was deeply skeptical of its correctness, emphasized that the evolution of quantum systems naturally leads to states that might be measured to have grossly different properties. His “Schrödinger cat” states, famously, scale up quantum uncertainty into questions about feline mortality. Prior to measurement, as we’ve seen in our examples, one cannot assign the property of life (or death) to the cat. Both — or neither — coexist within a netherworld of possibility.

Everyday language is ill suited to describe quantum complementarity, in part because everyday experience does not encounter it. Practical cats interact with surrounding air molecules, among other things, in very different ways depending on whether they are alive or dead, so in practice the measurement gets made automatically, and the cat gets on with its life (or death). But entangled histories describe q-ons that are, in a real sense, Schrödinger kittens. Their full description requires, at intermediate times, that we take both of two contradictory property-trajectories into account.

The controlled experimental realization of entangled histories is delicate because it requires we gather partial information about our q-on. Conventional quantum measurements generally gather complete information at one time — for example, they determine a definite shape, or a definite color — rather than partial information spanning several times. But it can be done — indeed, without great technical difficulty. In this way we can give definite mathematical and experimental meaning to the proliferation of “many worlds” in quantum theory, and demonstrate its substantiality.

This article was reprinted on Wired.com .

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September 20, 2022

Proving that quantum entanglement is real: Researcher answers questions about his historical experiments

by California Institute of Technology

In the 1930's when scientists, including Albert Einstein and Erwin Schrödinger, first discovered the phenomenon of entanglement, they were perplexed. Entanglement, disturbingly, required two separated particles to remain connected without being in direct contact. Einstein famously called entanglement "spooky action at a distance," since the particles seemed to be communicating faster than the speed of light.

To explain the bizarre implications of entanglement, Einstein, along with Boris Podolsky and Nathan Rosen (EPR), argued that "hidden variables" should be added to quantum mechanics to explain entanglement, and to restore "locality" and "causality" to the behavior of the particles. Locality states that objects are only influenced by their immediate surroundings. Causality states that an effect cannot occur before its cause, and that causal signaling cannot propagate faster than light-speed. Niels Bohr famously disputed EPR's argument, while Schrödinger and Wendell Furry, in response to EPR, independently hypothesized that entanglement vanishes with wide-particle separation.

Unfortunately, no experimental evidence for or against quantum entanglement of widely separated particles was available then. Experiments have since proven that entanglement is very real and fundamental to nature. Moreover, quantum mechanics has now been proven to work, not only at very short distances but also at very great distances. Indeed, China's quantum-encrypted communications satellite, Micius, relies on quantum entanglement between photons that are separated by thousands of kilometers.

The very first of these experiments was proposed and executed by Caltech alumnus John Clauser (BS '64) in 1969 and 1972, respectively. His findings are based on Bell's theorem, devised by CERN theorist John Bell. In 1964, Bell ironically proved that EPR's argument actually led to the opposite conclusion from what EPR had originally intended to show. Bell showed that quantum entanglement is, in fact, incompatible with EPR's notion of locality and causality.

In 1969, while still a graduate student at Columbia University, Clauser, along with Michael Horne, Abner Shimony, and Richard Holt, transformed Bell's 1964 mathematical theorem into a very specific experimental prediction via what is now called the Clauser–Horne–Shimony–Holt (CHSH) inequality (Their paper has been cited more than 8,500 times on Google Scholar.) In 1972, when he was a postdoctoral researcher at UC Berkeley and Lawrence Berkeley National Laboratory, Clauser and graduate student Stuart Freedman were the first to prove experimentally that two widely separated particles (about 10 feet apart) can be entangled. Clauser went on to perform three more experiments testing the foundations of quantum mechanics and entanglement, with each new experiment confirming and extending his results. The Freedman–Clauser experiment was the first test of the CHSH inequality. It has now been tested experimentally hundreds of times at laboratories around the world to confirm that quantum entanglement is real.

Clauser's work earned him the 2010 Wolf Prize in physics. He shared it with Alain Aspect of the Institut d' Optique and Ecole Polytechnique and Anton Zeilinger of the University of Vienna and the Austrian Academy of Sciences "for an increasingly sophisticated series of tests of Bell's inequalities, or extensions thereof, using entangled quantum states," according to the award citation.

Here, John Clauser answers questions about his historical experiments.

We hear that your idea of testing the principles of entanglement was unappealing to other physicists. Can you tell us more about that?

In the 1960s and 70s, experimental testing of quantum mechanics was unpopular at Caltech, Columbia, UC Berkeley, and elsewhere. My faculty at Columbia told me that testing quantum physics was going to destroy my career. While I was performing the 1972 Freedman–Clauser experiment at UC Berkeley, Caltech's Richard Feynman was highly offended by my impertinent effort and told me that it was tantamount to professing a disbelief in quantum physics. He arrogantly insisted that quantum mechanics is obviously correct and needs no further testing! My reception at UC Berkeley was lukewarm at best and was only possible through the kindness and tolerance of Professors Charlie Townes [Ph.D. '39, Nobel Laureate '64] and Howard Shugart [BS '53], who allowed me to continue my experiments there.

In my correspondence with John Bell, he expressed exactly the opposite sentiment and strongly encouraged me to do an experiment. John Bell's 1964 seminal work on Bell's theorem was originally published in the terminal issue of an obscure journal, Physics , and in an underground physics newspaper, Epistemological Letters . It was not until after the 1969 CHSH paper and the 1972 Freedman–Clauser results were published in the Physical Review Letters that John Bell finally openly discussed his work. He was aware of the taboo on questioning quantum mechanics' foundations and had never discussed it with his CERN co-workers.

What made you want to carry through with the experiments anyway?

Part of the reason that I wanted to test the ideas was because I was still trying to understand them. I found the predictions for entanglement to be sufficiently bizarre that I could not accept them without seeing experimental proof. I also recognized the fundamental importance of the experiments and simply ignored the career advice of my faculty. Moreover, I was having a lot of fun doing some very challenging experimental physics with apparatuses that I built mostly using leftover physics department scrap. Before Stu Freedman and I did the first experiment, I also personally thought that Einstein's hidden-variable physics might actually be right, and if it is, then I wanted to discover it. I found Einstein's ideas to be very clear. I found Bohr's rather muddy and difficult to understand.

What did you expect to find when you did the experiments?

In truth, I really didn't know what to expect except that I would finally determine who was right—Bohr or Einstein. I admittedly was betting in favor of Einstein but did not actually know who was going to win. It's like going to the racetrack. You might hope that a certain horse will win, but you don't really know until the results are in. In this case, it turned out that Einstein was wrong. In the tradition of Caltech's Richard Feynman and Kip Thorne [BS '62], who would place scientific bets, I had a bet with quantum physicist Yakir Aharonov on the outcome of the Freedman–Clauser experiment. Curiously, he put up only one dollar to my two. I lost the bet and enclosed a two-dollar bill and congratulations when I mailed him a preprint with our results.

I was very sad to see that my own experiment had proven Einstein wrong. But the experiment gave a 6.3-sigma result against him [a five-sigma result or higher is considered the gold standard for significance in physics]. But then Dick Holt and Frank Pipkin's competing experiment at Harvard (never published) got the opposite result. I wondered if perhaps I had overlooked some important detail. I went on alone at UC Berkeley to perform three more experimental tests of quantum mechanics. All yielded the same conclusions. Bohr was right, and Einstein was wrong. The Harvard result did not repeat and was faulty. When I reconnected with my Columbia faculty, they all said, "We told you so! Now stop wasting money and go do some real physics." At that point in my career, the only value in my work was that it demonstrated that I was a reasonably talented experimental physicist. That fact alone got me a job at Lawrence Livermore National Lab doing controlled-fusion plasma physics research.

Can you help us understand exactly what your experiments showed?

In order to clarify what the experiments showed, Mike Horne and I formulated what is now known as Clauser–Horne Local Realism [1974]. Additional contributions to it were subsequently offered by John Bell and Abner Shimony, so perhaps it is more properly called Bell–Clauser–Horne–Shimony Local Realism. Local Realism was very short-lived as a viable theory. Indeed, it was experimentally refuted even before it was fully formulated. Nonetheless, Local Realism is heuristically important because it shows in detail what quantum mechanics is not.

Local Realism assumes that nature consists of stuff, of objectively real objects, i. e., stuff you can put inside a box. (A box here is an imaginary closed surface defining separated inside and outside volumes.) It further assumes that objects exist whether or not we observe them. Similarly, definite experimental results are assumed to obtain, whether or not we look at them. We may not know what the stuff is, but we assume that it exists and that it is distributed throughout space. Stuff may evolve either deterministically or stochastically. Local Realism assumes that the stuff within a box has intrinsic properties, and that when someone performs an experiment within the box, the probability of any result that obtains is somehow influenced by the properties of the stuff within that box. If one performs say a different experiment with different experimental parameters, then presumably a different result obtains. Now suppose one has two widely separated boxes, each containing stuff. Local Realism further assumes that the experimental parameter choice made in one box cannot affect the experimental outcome in the distant box. Local Realism thereby prohibits spooky action-at-a-distance. It enforces Einstein's causality that prohibits any such nonlocal cause and effect. Surprisingly, those simple and very reasonable assumptions are sufficient on their own to allow derivation of a second important experimental prediction limiting the correlation between experimental results obtained in the separated boxes. That prediction is the 1974 Clauser–Horne (CH) inequality.

The 1969 CHSH inequality's derivation had required several minor supplementary assumptions, sometimes called "loopholes." The CH inequality's derivation eliminates those supplementary assumptions and is thus more general. Quantum entangled systems exist that disagree with the CH prediction, whereby Local Realism is amenable to experimental disproof. The CHSH and CH inequalities are both violated, not only by the first 1972 Freedman–Clauser experiment and my second 1976 experiment but now by literally hundreds of confirming independent experiments. Various labs have now entangled and violated the CHSH inequality with photon pairs, beryllium ion pairs, ytterbium ion pairs, rubidium atom pairs, whole rubidium-atom cloud pairs, nitrogen vacancies in diamonds, and Josephson phase qubits.

Testing Local Realism and the CH inequality was considered by many researchers to be important to eliminate the CHSH loopholes. Considerable effort was thus marshaled, as quantum optics technology improved and permitted. Testing the CH inequality had become a holy grail challenge for experimentalists. Violation of the CH inequality was finally achieved first in 2013 and again in 2015 at two competing laboratories: Anton Zeilinger's group at the University of Vienna, and Paul Kwiat's group at the University of Illinois at Urbana–Champaign. The 2015 experiments involved 56 researchers! Local Realism is now soundly refuted! The agreement between the experiments and quantum mechanics now firmly proves that nonlocal quantum entanglement is real.

What are some of the important technological applications of your work?

One application of my work is to the simplest possible object defined by Local Realism—a single bit of information. Local Realism shows that a single quantum mechanical bit of information, a "qubit," cannot always be localized in a space-time box. This fact provides the fundamental basis of quantum information theory and quantum cryptography. Caltech's quantum science and technology program, the 2019 $1.28-billion U.S. National Quantum Initiative, and the 2019 $400 million Israeli National Quantum Initiative all rely on the reality of entanglement. The Chinese Micius quantum-encrypted communications satellite system's configuration is almost identical to that of the Freedman–Clauser experiment. It uses the CHSH inequality to verify entanglement's persistence through outer space.

Journal information: Physical Review Letters

Provided by California Institute of Technology

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First Experimental Proof That Quantum Entanglement Is Real

A Q&A with Caltech alumnus John Clauser on his first experimental proof of quantum entanglement.

When scientists, including Albert Einstein and Erwin Schrödinger, first discovered the phenomenon of entanglement in the 1930s, they were perplexed. Disturbingly, entanglement required two separated particles to remain connected without being in direct contact. In fact, Einstein famously called entanglement “spooky action at a distance,” because the particles seemed to be communicating faster than the speed of light.

Born on December 1, 1942, John Francis Clauser is an American theoretical and experimental physicist known for contributions to the foundations of quantum mechanics, in particular the Clauser–Horne–Shimony–Holt inequality. Clauser was awarded the 2022 Nobel Prize in Physics, jointly with Alain Aspect and Anton Zeilinger “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.”

To explain the bizarre implications of entanglement, Einstein, along with Boris Podolsky and Nathan Rosen (EPR), argued that “hidden variables” should be added to quantum mechanics. These could be used to explain entanglement, and to restore “locality” and “causality” to the behavior of the particles. Locality states that objects are only influenced by their immediate surroundings. Causality states that an effect cannot occur before its cause, and that causal signaling cannot propagate faster than light speed. Niels Bohr famously disputed EPR’s argument, while Schrödinger and Wendell Furry, in response to EPR, independently hypothesized that entanglement vanishes with wide-particle separation.

Unfortunately, at the time, no experimental evidence for or against quantum entanglement of widely separated particles was available. Experiments have since proven that entanglement is very real and fundamental to nature. Furthermore, quantum mechanics has now been proven to work, not only at very short distances but also at very great distances. Indeed, China’s quantum-encrypted communications satellite, Micius, (part of the Quantum Experiments at Space Scale (QUESS) research project) relies on quantum entanglement between photons that are separated by thousands of kilometers.

The very first of these experiments was proposed and executed by Caltech alumnus John Clauser (BS ’64) in 1969 and 1972, respectively. His findings are based on Bell’s theorem, devised by CERN theorist John Bell. In 1964, Bell ironically proved that EPR’s argument actually led to the opposite conclusion from what EPR had originally intended to show. Bell demonstrated that quantum entanglement is, in fact, incompatible with EPR’s notion of locality and causality.

In 1969 , while still a graduate student at Columbia University , Clauser, along with Michael Horne, Abner Shimony, and Richard Holt, transformed Bell’s 1964 mathematical theorem into a very specific experimental prediction via what is now called the Clauser–Horne–Shimony–Holt (CHSH) inequality ( Their paper has been cited more than 8,500 times on Google Scholar .) In 1972, when he was a postdoctoral researcher at the University of California Berkeley and Lawrence Berkeley National Laboratory , Clauser and graduate student Stuart Freedman were the first to prove experimentally that two widely separated particles (about 10 feet apart) can be entangled.

Clauser went on to perform three more experiments testing the foundations of quantum mechanics and entanglement, with each new experiment confirming and extending his results. The Freedman–Clauser experiment was the first test of the CHSH inequality. It has now been tested experimentally hundreds of times at laboratories around the world to confirm that quantum entanglement is real.

Clauser’s work earned him the 2010 Wolf Prize in physics. He shared it with Alain Aspect of the Institut d’ Optique and Ecole Polytechnique and Anton Zeilinger of the University of Vienna and the Austrian Academy of Sciences “for an increasingly sophisticated series of tests of Bell’s inequalities, or extensions thereof, using entangled quantum states,” according to the award citation.

Here, John Clauser answers questions about his historical experiments.

We hear that your idea of testing the principles of entanglement was unappealing to other physicists. Can you tell us more about that?

In the 1960s and 70s, experimental testing of quantum mechanics was unpopular at Caltech, Columbia, UC Berkeley, and elsewhere. My faculty at Columbia told me that testing quantum physics was going to destroy my career. While I was performing the 1972 Freedman–Clauser experiment at UC Berkeley, Caltech’s Richard Feynman was highly offended by my impertinent effort and told me that it was tantamount to professing a disbelief in quantum physics. He arrogantly insisted that quantum mechanics is obviously correct and needs no further testing! My reception at UC Berkeley was lukewarm at best and was only possible through the kindness and tolerance of Professors Charlie Townes [PhD ’39, Nobel Laureate ’64] and Howard Shugart [BS ’53], who allowed me to continue my experiments there.

In my correspondence with John Bell , he expressed exactly the opposite sentiment and strongly encouraged me to do an experiment. John Bell’s 1964 seminal work on Bell’s theorem was originally published in the terminal issue of an obscure journal, Physics , and in an underground physics newspaper, Epistemological Letters . It was not until after the 1969 CHSH paper and the 1972 Freedman–Clauser results were published in the Physical Review Letters that John Bell finally openly discussed his work. He was aware of the taboo on questioning quantum mechanics’ foundations and had never discussed it with his CERN co-workers.

What made you want to carry through with the experiments anyway?

Part of the reason that I wanted to test the ideas was because I was still trying to understand them. I found the predictions for entanglement to be sufficiently bizarre that I could not accept them without seeing experimental proof. I also recognized the fundamental importance of the experiments and simply ignored the career advice of my faculty. Moreover, I was having a lot of fun doing some very challenging experimental physics with apparatuses that I built mostly using leftover physics department scrap. Before Stu Freedman and I did the first experiment, I also personally thought that Einstein’s hidden-variable physics might actually be right, and if it is, then I wanted to discover it. I found Einstein’s ideas to be very clear. I found Bohr’s rather muddy and difficult to understand.

What did you expect to find when you did the experiments?

In truth, I really didn’t know what to expect except that I would finally determine who was right—Bohr or Einstein. I admittedly was betting in favor of Einstein but did not actually know who was going to win. It’s like going to the racetrack. You might hope that a certain horse will win, but you don’t really know until the results are in. In this case, it turned out that Einstein was wrong. In the tradition of Caltech’s Richard Feynman and Kip Thorne [BS ’62], who would place scientific bets, I had a bet with quantum physicist Yakir Aharonov on the outcome of the Freedman–Clauser experiment. Curiously, he put up only one dollar to my two. I lost the bet and enclosed a two-dollar bill and congratulations when I mailed him a preprint with our results.

I was very sad to see that my own experiment had proven Einstein wrong. But the experiment gave a 6.3-sigma result against him [a five-sigma result or higher is considered the gold standard for significance in physics]. But then Dick Holt and Frank Pipkin’s competing experiment at Harvard (never published) got the opposite result. I wondered if perhaps I had overlooked some important detail. I went on alone at UC Berkeley to perform three more experimental tests of quantum mechanics. All yielded the same conclusions. Bohr was right, and Einstein was wrong. The Harvard result did not repeat and was faulty. When I reconnected with my Columbia faculty, they all said, “We told you so! Now stop wasting money and go do some real physics.” At that point in my career, the only value in my work was that it demonstrated that I was a reasonably talented experimental physicist. That fact alone got me a job at Lawrence Livermore National Lab doing controlled-fusion plasma physics research.

Can you help us understand exactly what your experiments showed?

In order to clarify what the experiments showed, Mike Horne and I formulated what is now known as Clauser–Horne Local Realism [ 1974 ]. Additional contributions to it were subsequently offered by John Bell and Abner Shimony , so perhaps it is more properly called Bell–Clauser–Horne–Shimony Local Realism . Local Realism was very short-lived as a viable theory. Indeed, it was experimentally refuted even before it was fully formulated. Nonetheless, Local Realism is heuristically important because it shows in detail what quantum mechanics is not .

Local Realism assumes that nature consists of stuff, of objectively real objects, i.e., stuff you can put inside a box. (A box here is an imaginary closed surface defining separated inside and outside volumes.) It further assumes that objects exist whether or not we observe them. Similarly, definite experimental results are assumed to obtain, whether or not we look at them. We may not know what the stuff is, but we assume that it exists and that it is distributed throughout space. Stuff may evolve either deterministically or stochastically. Local Realism assumes that the stuff within a box has intrinsic properties, and that when someone performs an experiment within the box, the probability of any result that obtains is somehow influenced by the properties of the stuff within that box. If one performs say a different experiment with different experimental parameters, then presumably a different result obtains. Now suppose one has two widely separated boxes, each containing stuff. Local Realism further assumes that the experimental parameter choice made in one box cannot affect the experimental outcome in the distant box. Local Realism thereby prohibits spooky action-at-a-distance. It enforces Einstein’s causality that prohibits any such nonlocal cause and effect. Surprisingly, those simple and very reasonable assumptions are sufficient on their own to allow derivation of a second important experimental prediction limiting the correlation between experimental results obtained in the separated boxes. That prediction is the 1974 Clauser–Horne (CH) inequality.

The 1969 CHSH inequality’s derivation had required several minor supplementary assumptions, sometimes called “loopholes.” The CH inequality’s derivation eliminates those supplementary assumptions and is thus more general. Quantum entangled systems exist that disagree with the CH prediction, whereby Local Realism is amenable to experimental disproof. The CHSH and CH inequalities are both violated, not only by the first 1972 Freedman–Clauser experiment and my second 1976 experiment but now by literally hundreds of confirming independent experiments. Various labs have now entangled and violated the CHSH inequality with photon pairs, beryllium ion pairs, ytterbium ion pairs, rubidium atom pairs, whole rubidium-atom cloud pairs, nitrogen vacancies in diamonds, and Josephson phase qubits.

Testing Local Realism and the CH inequality was considered by many researchers to be important to eliminate the CHSH loopholes. Considerable effort was thus marshaled, as quantum optics technology improved and permitted. Testing the CH inequality had become a holy grail challenge for experimentalists. Violation of the CH inequality was finally achieved first in 2013 and again in 2015 at two competing laboratories: Anton Zeilinger’s group at the University of Vienna, and Paul Kwiat’s group at the University of Illinois at Urbana–Champaign. The 2015 experiments involved 56 researchers! Local Realism is now soundly refuted! The agreement between the experiments and quantum mechanics now firmly proves that nonlocal quantum entanglement is real.

What are some of the important technological applications of your work?

One application of my work is to the simplest possible object defined by Local Realism—a single bit of information. Local Realism shows that a single quantum mechanical bit of information, a “qubit,” cannot always be localized in a space-time box. This fact provides the fundamental basis of quantum information theory and quantum cryptography. Caltech’s quantum science and technology program, the 2019 $1.28-billion U.S. National Quantum Initiative, and the 2019 $400 million Israeli National Quantum Initiative all rely on the reality of entanglement. The Chinese Micius quantum-encrypted communications satellite system’s configuration is almost identical to that of the Freedman–Clauser experiment. It uses the CHSH inequality to verify entanglement’s persistence through outer space.

Can you tell us more about your family’s strong connection with Caltech?

My dad, Francis H. Clauser [BS ’34, MS ’35, PhD ’37, Distinguished Alumni Award ’66] and his brother Milton U. Clauser [BS ’34, MS ’35, PhD ’37] were PhD students at Caltech under Theodore von Kármán . Francis Clauser was Clark Blanchard Millikan Professor of Engineering at Caltech (Distinguished Faculty Award ’80) and chair of Caltech’s Division of Engineering and Applied Science. Milton U. Clauser’s son, Milton J. Clauser [PhD ’66], and grandson, Karl Clauser [BS ’86] both went to Caltech. My mom, Catharine McMillan Clauser was Caltech’s humanities librarian, where she met my dad. Her brother, Edwin McMillan [BS ’28, MS ’29], is a Caltech alum and ’51 Nobel Laureate. The family now maintains Caltech’s “Milton and Francis Doctoral Prize” awarded at Caltech commencements.

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Quantum squeezing: at the edge of physics, quantum ghosts: atoms become transparent to certain frequencies of light, ask a caltech expert: physicists explain quantum gravity, physicists observe and control quantum motion, experiment shows that light defies the principles of classical physics, “schrödinger’s hat” conceals matter waves inside an invisible container, simulating quantum walks in two dimensions, evidence of elusive majorana fermions raises possibilities for quantum computing, higgs boson signals gain strength at large hadron collider, 21 comments.

The interactions and balances of topological vortex fields cover all short-distance and long-distance contributions, and are the basis of the formation and evolution of cosmic matter. 1.According to the topological vortex field theory, not only light, almost all rays and particles have electric effects. 2.The nature of electricity is perfect fluid.It has no shear stresses,viscosity,or heat conduction.Electric current generates heat because it interacts with vortex current. 3.Entanglement is one of the forms of interaction between vortexes. 4.If you are interested, please see https://zhuanlan.zhihu.com/p/463666584 . Good luck to your team.

The physical characteristics of the fluid vortex center are suitable to be described by energy rather than mass. According to the topological vortex field theory, there are two types of vortex centers: one is constant temperature and the other is variable temperature.

The expansion of space is due to star dynamics or relativity is a part of this.So,entanglement is a natural property present uniformly in universe for quantum particle after adding,saý GR(but not essential beside an arbitrary rational standard taken for measurement in the experiment);hence speed of light has no relation for entanglment of quantum particles at any two points in the same galaxy,or else.These facts have well proven before by many experimentations and are in due course of appĺied field,thus nothing to state about noble prize of current year in physics,but taken as secoded phenomena of the principle of entanglement.Congratulations to the physicists for their good presentations and wise works,granted late.

Fascinating!!!

Quantum Entanglement is perhaps the strangest phenomenon in physics, when some small particles may communicate with each other instantly and over vast distances. How can that happen without violating the maximum speed in the universe, the speed of light?

As this article says, the two ways physicists have used to answer this, that the particles contain hidden variables of unknown natures and that the universe is completely deterministic with all results predefined, have been shown to be incorrect.

Perhaps concepts in String Theory can help. There are 11 possible dimensions in String Theory and I suggest one of them leads a way around, what Einstein called this “spooky action at a distance”. Specifics on this can be found by searching YouTube for “Quantum Entanglement – A String Theory Way”

Bùt credìt of research on particle physics goes for quark-gluon to the America,charm quark to the CERN particĺe physicists.Thus,spin or magnetism required for entanglement has been done in parallel is an established work.

GR in connection to star dynamics is well proven concept taken in all kinds of measurements.

Metaphysics in Quantum Computation field is usual natural part has also been proven and established by experimentation.

All these are distinct works present ofcourse in fractional forms,but commonly adopted jointly in Quantum Computation.

So,alĺ these discoveries with their applications express happiness on behalf of this year’s Physics Nobel Prize with gratefulness to community and all with thanks.

It’s so fascinating contemplating the theme and variations of line of sight communication being moot through the newer mechanical developments

Energy can not be created or destroyed. Our thoughts are forms of energy. And scripture says “as a man think so is he”. Negative thoughts create depression, lack and poverty. Positive thoughts create abundance, wealth and prosperity.

FTL effects and hidden variable are not clearly ruled out and failure of localism could arise from FTL effects, it seems. “Non-local” with “hidden variables” still point to invisible FTL gravity effects, I believe.

Just to clarify, I wanted to note that it still seems “non-localism” and “hidden variables” can fit FTL gravity effects.

Refraction of fire and chief fields to contain high density gravity using quantum Magnetic codings will intensify the field of gravity to project

Quantum energy and its distant entanglement might be a breakthrough for holistic medical science. So therefore mysteries of working of homeopathic remedies on living organisms including humans could be explained and placebo effects of homeopathic remedies can further be explored. Diversity of conventional medical treatment can be boxed into single holistic approach. Thumbs up to marvelous discovery.

I have found a name for what goes on in my mind

ha ha ha… It’s the bizarre world where those embarrassments attempt to qualify as an authority by making word salad… to use their deleterious language once reserved for those sacrifices for the greater good, fire pits, abattoirs, and bomb vests. China still kills them, an economic champion, at what sacrifice? But you may be talking of mirror neurons, that not critical part of physical motion that allows instant … ok. entanglement for such as line dancers, but don’t confuse that with your critical thinking. Remember mirror neurons don’t really care, it’s a temporary allowing of one’s trust to be like another, not forebrain activity.

There is, of course, an information ‘matrix’ associated with the isotropic energy substrate underlying all measurable phenomena. ‘Particles’, therefore, isuue from this substrate and have, ipso facto, access to the information at any point of manifestation. It seems to me. So, no problem really with ‘Spooky Action’.

‘Particles’ isuue from this substrate put this notion well. The interactions and balances of topological vortex fields cover all short-distance and long-distance contributions, wich are the substrate of the formation and evolution of cosmic matter.

There are many here who are eminently more qualified than myself but it seems “apparent” that particles simultaneously exist in a different dimension and in that different dimension are essentially quite local.

you guys are just figuring this whole thing out now, this whole thing had been figured out a long time ago by ancient spiritualism, probably over 10 000 years ago. ancient spirituality had been trying to tell humanity that there is another dimension( “invisible reality”) which is the source of all things happening in this universe and outside the universe, they call it “the all”, some spiritual traditions call it the infinite consciousness, non-duality, the timeless dimension, the formless dimension and more. What’s happening in this universe of relativity is ultimately an illusion because people perceive reality as separate entities and the dimension I’m talking about is beyond forms, time, and space which all the dualistic categories of this universe and mental principles ceases to exist and what left is pure energy, the existence of this present moment(now).thats what science is trying to figure out and spirituality had already figure this whole thing out very long time ago. if someone wants to figure out what’s going on in quantum entanglement, I highly recommend you to access spirituality and non-dual teachings. it is not surprising that science is shocked about this because this whole had been figured out a long time ago, it’s just that science is catching up with spirituality. whatever is happening in the phenomenon of quantum entanglement that seems spooky is governed by that invisible reality called infinite conscioussness, which you cannot understand conceptually but realize as the oness.

Pure drivel, to start with Einstien who this fraudulent author misquotes, said quantum entanglement DOESN’T occur and there was no spooky action at a distance… completely misquoting others and besmirching their names by such slanders is common among such complete frauds as By CALIFORNIA INSTITUTE OF TECHNOLOGY or Not?

Just saying, anyone else ever seen a supposedly academic publication without a long list of authors, and co-authors all wanting credit for the publication as well as a long list of citations? No? Also the long list of word salad comments, anything false spawns false, proof of contraction is abundant, no such thing as quantum entanglement.

i suspect the quantum entanglement experiments are flawed but I have not found the details of these experiments. My skepticism arises from theories surrounding the origin of the universe. Black holes are gravitationally sorted spheres with the densest particles in the center. In order to have a big bang black holes (remnants of adjacent universes would have to collide. The resulting explosion propelled particles into space while preserving some of the more dense particles from the core which formed the early galaxies. The bulk of the mass shot into space the gavitational force decreasing with greater volume and distance from the center dense particles resulting in acceleration. No dark matter required. I am also skeptical of the atomic clock experiment which showed time slows with speed. all the experiment shows is that atomic radius is not constant. As an atom approaches the dense matter from the big bang at the center of the earth its radius deceases. I also suspect the current pole rotation we are in is tied to pre big bang dense matter at the center of the earth, and does not involve liquid iron suddenly changing direction. If quantum entanglement is real the experimental proceedures should be published and available to the layman.

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• Research update

Open problem in quantum entanglement theory solved after nearly 25 years

A quarter of a century after it was first posed, a fundamental question about the nature of quantum entanglement finally has an answer – and that answer is “no”. In a groundbreaking study, Julio I de Vicente from the Universidad Carlos III de Madrid, Spain showed that so-called maximally entangled mixed states for a fixed spectrum do not always exist , challenging long-standing assumptions in quantum information theory in a way that has broad implications for quantum technologies.

Since the turn of the millennium, the Institute for Quantum Optics and Quantum Information (IQOQI) in Vienna, Austria, has maintained a conspicuous list of open problems in the quantum world. Number 5 on this list asks: “Is it true that for arbitrary entanglement monotones one gets the same maximally entangled states among all density operators of two qubits with the same spectrum?” In simpler terms, this question is essentially asking whether a quantum system can maintain its maximally entangled state in a realistic scenario, where noise is present.

This question particularly suited de Vicente, who has long been fascinated by foundational issues in quantum theory and is drawn to solving well-defined mathematical problems. Previous research had suggested that such a maximally entangled mixed state might exist for systems of two qubits (quantum bits), thereby maximizing multiple entanglement measures. In a study published in Physical Review Letters , however, de Vicente concludes otherwise, demonstrating that for certain rank-2 mixed states, no state can universally maximize all entanglement measures across all states with the same spectrum.

“I had tried other approaches to this problem that turned out not to work,” de Vicente tells Physics World. “However, once I came up with this idea, it was very quick to see that this gave the solution. I can say that I felt very excited seeing that such a relatively simple argument could be used to answer this question.”

Importance of entanglement

Mathematics aside, what does this result mean for real-world applications and for physics? Well, entanglement is a unique quantum phenomenon with no classical counterpart, and it is essential for various quantum technologies. Since our present experimental reach is limited to a restricted set of quantum operations, entanglement is also a resource, and a maximally entangled state (meaning one that maximizes all measures of entanglement) is an especially valuable resource.

One example of a maximally entangled state is a Bell state, which is one of four possible states for a system of two qubits that are each in a superposition of 0 and 1. Bell states are pure states, meaning that they can, in principle, be known with complete precision. This doesn’t necessarily mean they have definite values for properties like energy and momentum, but it distinguishes them from a statistical mixture of different pure states.

Maximally entangled mixed states

The concept of maximally entangled mixed states (MEMS) is a departure from the traditional view of entanglement, which has been primarily associated with pure states. Conceptually, when we talk about a pure state, we imagine a scenario where a device consistently produces the same quantum state through a specific preparation process. However, practical scenarios often involve mixed states due to noise and other factors.

In effect, MEMS are a bridge between theoretical models and practical applications, offering robust entanglement even in less-than-ideal conditions. This makes them particularly valuable for technologies like quantum encryption and quantum computing, where maintaining entanglement is crucial for performance.

de Vicente’s result relies on an entanglement measure that is constructed ad hoc and has no clear operational meaning. A more relevant version of this result for applications, he says, would be to “identify specific quantum information protocols where the optimal state for a given level of noise is indeed different”.

Entanglement gets hot and messy

While de Vicente’s finding addresses an existing question, it also introduces several new ones, such as the conditions needed to simultaneously optimize various entanglement measures within a system. It also raises the possibility of investigating whether de Vicente’s theorems hold under other notions of “the same level of noise”, particularly if these arise in well-defined practical contexts.

The implications of this research extend beyond theoretical physics. By enabling better control and manipulation of quantum states, MEMS could revolutionize how we approach problems in quantum mechanics, from computing to material science. Now that we understand their limitations better, researchers are poised to explore their potential applications, including their role in developing quantum technologies that are robust, scalable, and practical.

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Entanglement-based quantum information technology: a tutorial

Research output : Contribution to journal › Article › peer-review

Entanglement is a quintessential quantum mechanical phenomenon with no classical equivalent. First discussed by Einstein, Podolsky, and Rosen and formally introduced by Schrödinger in 1935, entanglement has grown from a scientific debate to a radically new resource that sparks a technological revolution. This review focuses on fundamentals and recent advances in entanglement-based quantum information technology (QIT), specifically in photonic systems. Photons are unique quantum information carriers with several advantages, such as their ability to operate at room temperature, their compatibility with existing communication and sensing infrastructures, and the availability of readily accessible optical components. Photons also interface well with other solid-state quantum platforms. We first provide an overview on entanglement, starting with an introduction to its development from a historical perspective followed by the theory for entanglement generation and the associated representative experiments. We then dive into the applications of entanglement-based QIT for sensing, imaging, spectroscopy, data processing, and communication. Before closing, we present an outlook for the architecture of the next-generation entanglement-based QIT and its prospective applications.

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• Atomic and Molecular Physics, and Optics

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T1 - Entanglement-based quantum information technology

T2 - a tutorial

AU - Zhang, Zheshen

AU - You, Chenglong

AU - Magaña-Loaiza, Omar S.

AU - Fickler, Robert

AU - León-Montiel, Roberto de J.

AU - Torres, Juan P.

AU - Humble, Travis S.

AU - Liu, Shuai

AU - Xia, Yi

AU - Zhuang, Quntao

N1 - Publisher Copyright: © 2024 Optica Publishing Group (formerly OSA). All rights reserved.

PY - 2024/3/31

Y1 - 2024/3/31

N2 - Entanglement is a quintessential quantum mechanical phenomenon with no classical equivalent. First discussed by Einstein, Podolsky, and Rosen and formally introduced by Schrödinger in 1935, entanglement has grown from a scientific debate to a radically new resource that sparks a technological revolution. This review focuses on fundamentals and recent advances in entanglement-based quantum information technology (QIT), specifically in photonic systems. Photons are unique quantum information carriers with several advantages, such as their ability to operate at room temperature, their compatibility with existing communication and sensing infrastructures, and the availability of readily accessible optical components. Photons also interface well with other solid-state quantum platforms. We first provide an overview on entanglement, starting with an introduction to its development from a historical perspective followed by the theory for entanglement generation and the associated representative experiments. We then dive into the applications of entanglement-based QIT for sensing, imaging, spectroscopy, data processing, and communication. Before closing, we present an outlook for the architecture of the next-generation entanglement-based QIT and its prospective applications.

AB - Entanglement is a quintessential quantum mechanical phenomenon with no classical equivalent. First discussed by Einstein, Podolsky, and Rosen and formally introduced by Schrödinger in 1935, entanglement has grown from a scientific debate to a radically new resource that sparks a technological revolution. This review focuses on fundamentals and recent advances in entanglement-based quantum information technology (QIT), specifically in photonic systems. Photons are unique quantum information carriers with several advantages, such as their ability to operate at room temperature, their compatibility with existing communication and sensing infrastructures, and the availability of readily accessible optical components. Photons also interface well with other solid-state quantum platforms. We first provide an overview on entanglement, starting with an introduction to its development from a historical perspective followed by the theory for entanglement generation and the associated representative experiments. We then dive into the applications of entanglement-based QIT for sensing, imaging, spectroscopy, data processing, and communication. Before closing, we present an outlook for the architecture of the next-generation entanglement-based QIT and its prospective applications.

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DO - 10.1364/AOP.497143

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JF - Advances in Optics and Photonics

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Quantum Computing for Beginners: Where to Start?

Quantum computing is an exciting and rapidly evolving field that promises to revolutionize technology and transform our understanding of computation. Unlike classical computers, which use bits as the smallest unit of information, quantum computers use quantum bits, or qubits, which can exist in multiple states simultaneously. This fundamental difference enables quantum computers to solve certain types of problems exponentially faster than classical computers. For beginners who are intrigued by the potential of quantum computing and want to understand its basics, this article will help you navigate where to start, what to learn, and how to build a solid foundation in this cutting-edge field.

Understanding Quantum Computing: The Basics

At its core, quantum computing is based on the principles of quantum mechanics, a branch of physics that describes the behavior of matter and energy at the smallest scales—at the level of atoms and subatomic particles. In classical computing, a bit is a binary unit that can be in one of two states: 0 or 1. However, in quantum computing, qubits can be in a state of 0, 1, or both simultaneously, a phenomenon known as superposition.

Superposition allows quantum computers to perform many calculations at once, making them extraordinarily powerful for specific tasks. In addition to superposition, quantum computing also relies on two other principles: entanglement and quantum interference. Entanglement is a phenomenon where two or more qubits become interconnected in such a way that the state of one qubit is dependent on the state of another, no matter how far apart they are. Quantum interference, on the other hand, enables quantum computers to amplify the correct answers and cancel out incorrect ones during computation.

Why is Quantum Computing Important?

Quantum computing holds the promise of solving problems that are currently intractable for classical computers. These problems include cryptographic challenges, complex optimization problems, and simulations of quantum physical processes such as molecular modeling. For example, quantum computers could potentially break traditional encryption methods by factoring large prime numbers much more efficiently than classical computers. They could also simulate the behavior of complex molecules in chemistry and materials science, enabling breakthroughs in drug discovery, materials design, and more.

In addition to these practical applications, quantum computing is also driving innovation in fundamental research across disciplines such as physics, computer science, mathematics, and engineering. As the technology matures, we can expect quantum computing to revolutionize fields like artificial intelligence , cybersecurity, financial modeling, and logistics optimization, among others.

Key Concepts to Grasp

To start your journey into quantum computing, it’s essential to familiarize yourself with a few foundational concepts. These include:

Qubits and Quantum States : Understanding the nature of qubits, superposition, and entanglement is crucial. Qubits are typically represented as vectors in a complex vector space, and their state can be visualized on the Bloch sphere, which provides a geometrical representation of their quantum state.

Quantum Gates and Circuits : Quantum gates are the building blocks of quantum algorithms , just as logic gates are the building blocks of classical algorithms. Quantum circuits are collections of quantum gates that manipulate qubits to perform computations. Unlike classical gates, which are deterministic, quantum gates are often reversible and operate on the principles of quantum mechanics.

Quantum Algorithms : Quantum algorithms leverage the properties of qubits to perform computations more efficiently than classical algorithms for certain tasks. Some of the most well-known quantum algorithms include Shor’s algorithm for integer factorization, Grover’s algorithm for unstructured search, and the quantum Fourier transform.

Quantum Error Correction : Due to the delicate nature of quantum states, quantum computers are highly susceptible to errors caused by decoherence and noise. Quantum error correction is a critical area of research aimed at developing techniques to detect and correct these errors to ensure reliable computation.

Where to Start Your Learning Journey

Stp 1: Build a Solid Foundation in Classical Computing and Mathematics

Before diving into quantum computing, it is essential to have a solid understanding of classical computing principles and foundational mathematics. Knowledge of algorithms, data structures, and computer architecture will be highly beneficial. Familiarity with linear algebra, probability theory, complex numbers, and calculus is also crucial, as these mathematical concepts form the backbone of quantum mechanics and quantum computing.

Step 2: Explore Quantum Mechanics Fundamentals

Since quantum computing is built on the principles of quantum mechanics, gaining a basic understanding of quantum mechanics is a necessary step. Begin with introductory quantum mechanics topics such as wave-particle duality, Heisenberg’s uncertainty principle, Schrödinger's equation, and the concepts of superposition and entanglement. There are numerous online courses, textbooks, and resources available that provide a gentle introduction to these complex concepts.

Step 3: Learn Quantum Computing Basics

Once you have a grasp of the necessary classical computing and quantum mechanics concepts, you can start learning the basics of quantum computing. There are several resources available for beginners, including online courses, tutorials, and textbooks. Some popular platforms for learning quantum computing include edX, Coursera, and MIT OpenCourseWare. You can also find quantum computing courses on platforms like Brilliant, which provide interactive and gamified learning experiences.

Start with beginner-friendly courses that introduce the fundamental principles of quantum computing, such as qubits, quantum gates, and quantum circuits. These courses often use visual tools and interactive simulations to help you grasp the abstract concepts involved.

Step 4: Experiment with Quantum Programming

Quantum programming is a unique challenge that involves creating algorithms and programs that run on quantum computers. One of the best ways to learn is by doing. Familiarize yourself with quantum programming languages and frameworks such as Qiskit (IBM), Cirq (Google), and Q# (Microsoft). These platforms provide access to quantum simulators and real quantum hardware, allowing you to write and execute your quantum programs.

Start by implementing simple quantum algorithms, such as the Deutsch-Jozsa algorithm or Grover’s search algorithm, to build your understanding of quantum programming paradigms. There are many open-source repositories, documentation, and community forums that provide guidance and support for beginners.

Step 5: Participate in Quantum Computing Communities and Hackathons

Joining a community can significantly accelerate your learning process. Participate in online forums, attend webinars, and join social media groups focused on quantum computing. Many quantum computing companies, like IBM, Microsoft , and Google, host community events, hackathons, and competitions that are open to beginners. These events provide a hands-on learning environment and allow you to network with professionals and enthusiasts in the field.

Step 6: Keep Up with the Latest Research and Developments

Quantum computing is a fast-evolving field with continuous advancements and discoveries. To stay updated, read research papers, attend conferences, and subscribe to quantum computing journals or newsletters. Websites like arXiv.org and Quantum Computing Report provide access to the latest research and publications. Understanding cutting-edge research can give you insights into emerging trends, new quantum algorithms, and novel hardware developments.

Recommended Learning Resources

There are several excellent resources to help you get started with quantum computing. Some recommended books include:

"Quantum Computation and Quantum Information" by Michael Nielsen and Isaac Chuang : Often referred to as the "Bible" of quantum computing, this book provides a comprehensive introduction to the theory and applications of quantum computation and quantum information.

"An Introduction to Quantum Computing" by Phillip Kaye, Raymond Laflamme, and Michele Mosca : A beginner-friendly book that introduces the key concepts and mathematical framework of quantum computing.

"Programming Quantum Computers" by Eric R. Johnston, Nic Harrigan, and Mercedes Gimeno-Segovia : This book provides practical guidance on quantum programming, including hands-on exercises using the Qiskit and Cirq frameworks.

For online resources, consider:

IBM Quantum Experience : IBM offers a free platform for learning and experimenting with quantum computing. It includes tutorials, a cloud-based quantum computer, and an active community.

Qiskit Documentation and Tutorials : Qiskit, an open-source quantum computing framework developed by IBM, offers extensive documentation, tutorials, and community resources.

Quantum Katas by Microsoft : A collection of programming exercises that help you learn quantum computing concepts through coding.

Preparing for a Future in Quantum Computing

Quantum computing is still in its early stages, and there are plenty of opportunities to contribute to its development. As a beginner, focus on building a strong foundation in the fundamental concepts of quantum mechanics and quantum computing. Develop your programming skills, particularly in quantum programming languages , and stay engaged with the quantum community.

Whether you aim to become a quantum software developer, researcher, or even a quantum hardware engineer, the skills you acquire today will prepare you for the rapidly evolving future of quantum computing. Stay curious, keep learning, and don't be afraid to dive deep into the fascinating world of quantum technology.

Starting your journey into quantum computing may seem daunting, but with the right approach and resources, it can be an incredibly rewarding experience. Begin with the basics of classical computing and quantum mechanics, then explore the core concepts of quantum computing, such as qubits, quantum gates, and quantum algorithms. Experiment with quantum programming, engage with communities and keep up with the latest research. As you build your knowledge and skills, you'll be better equipped to contribute to this groundbreaking field and be a part of the quantum revolution.

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• Published: 03 September 2024

Quantum double slit experiment with reversible detection of photons

• Vipin Devrari 1 &
• Mandip Singh 1  

Scientific Reports volume  14 , Article number:  20438 ( 2024 ) Cite this article

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• Quantum mechanics
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Principle of quantum superposition permits a photon to interfere with itself. As per the principle of causality, a photon must pass through the double-slit prior to its detection on the screen to exhibit interference. In this paper, a double-slit quantum interference experiment with reversible detection of Einstein–Podolsky–Rosen quantum entangled photons is presented. Where a photon is first detected on a screen without passing through a double-slit, while the second photon is propagating towards the double-slit. A detection event on the screen cannot affect the second photon with any signal propagating at the speed of light, even after its passage through the double-slit. After the detection of the first photon on the screen, the second photon is either passed through the double-slit or diverted towards a stationary photon detector. Therefore, the question of whether the first photon carries the which-path information of the second photon in the double-slit is eliminated. No single photon interference is exhibited by the second photon, even if another screen is placed after the double-slit.

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Quantum double-double-slit experiment with momentum entangled photons

Which-way identification by an asymmetrical double-slit experiment with monochromatic photons

Revisiting self-interference in Young’s double-slit experiments

Introduction.

In 1801, Young’s double-slit interference experiment proved that light behaves as a wave 1 , 2 . A first experimental observation of interference with very low intensity of light was reported by Taylor 3 . However, quantum mechanically, light consists of discrete energy packets known as photons, which can exhibit particle- or wave-like behaviour. According to the principle of quantum superposition, a single particle can exist at different locations simultaneously 4 , 5 . This counter-intuitive law of nature gives wave nature to a particle, and by its consequence, a particle can interfere with itself, i.e. all quantum superimposed states of a particle interfere with each other. In a single particle quantum double-slit experiment, a single particle is passed through a double-slit, and an interference pattern gradually emerges on the screen by accumulating particle detections by repeating the experiment. Each detection of a particle on the screen determines its position on the screen, whereas this measurement cannot determine the path of a particle in the double-slit. However, the interference pattern cannot be formed, when the which-path information of a particle is measured or stored by modifying the experiment. The casual temporal order of this experiment signifies a detection on the screen after the passage of a particle through the double-slit. This casual self interference was demonstrated experimentally with electrons 6 , 7 , 8 , 9 , neutrons 10 , 11 , photons 12 , 13 and positrons 14 . Quantum mechanics exerts no restriction on the self interference of macromolecules, which is experimentally demonstrated 15 , 16 , 17 , 18 , 19 , 20 . An experiment demonstrating self interference of two-photon amplitudes in a double-double-slit is performed with momentum entangled photons 21 , 22 . Another version of a double-slit experiment is realised by placing a double-slit in the path of one photon, where the interference pattern is formed only when both photons are measured 23 , 24 , 25 , 26 , 27 , 28 , 29 . However, in these experiments, both photons are measured after one of them is passed through the double-slit.

In this paper, a quantum double-slit experiment with reversible detection of photons is presented, which is carried out with continuous variable Einstein–Podolsy–Rosen (EPR) 30 quantum entangled photon pairs. A reversible detection implies that a photon of a quantum entangled pair is first detected on a screen while the other photon is propagating towards a double-slit, and later it can pass either through the double-slit or it can be diverted towards a stationary single photon detector. The experiment is configured such that the detection of a first photon on the screen cannot affect the second photon through any local communication, even after its interaction with the double-slit. This is because the second photon is separated from the detection event by a lightlike interval. Since the second photon passes through the double-slit after the detection of the first photon therefore, the first photon carried no which-path information of the second photon in the double-slit. The second photon is detected by stationary single photon detectors, which are placed at fixed locations throughout the interference experiment. The interference pattern is produced on the screen by repeating the experiment each time with a new EPR entangled pair, provided those photon detections on the screen are considered when the second photon is detected by a stationary detector positioned after the double-slit. However, position measurements of individual photons do not produce any interference pattern, even if the detector placed after the double-slit is displaced gradually to count photons at different locations. The experiment is performed with continuous variable EPR entangled photon pairs produced simultaneously in a Beta Barium Borate (BBO) nonlinear crystal by Type-I spontaneous parametric down conversion (SPDC) in a noncollinear configuration 31 , 32 , 33 , 34 , 35 , 36 , 37 . A real double-slit is used in this experiment, whereas the quantum entangled pair production rate is intentionally reduced to keep one entangled photon pair in the experiment until its detection. The second EPR entangled pair of photons is produced considerably later than the detection of the first entangled pair of photons. In addition, this paper presents a theoretical analysis of the experiment.

Concept and analysis

The EPR state is a continuous variable entangled quantum state of two particles, where both particles are equally likely to exist at all position and momentum locations. A one-dimensional EPR state in position basis is written as \(|\alpha \rangle =\int ^{\infty }_{-\infty }|x\rangle _{1}|x+{\textbf {x}}_{o}\rangle _{2} \textrm{d}x\) , where subscripts 1 and 2 represent particle-1 and particle-2, respectively. A constant \({\textbf {x}}_{o}\) corresponds to the position difference of particles. The same EPR state is expressed in momentum basis as \(|\alpha \rangle =\int ^{\infty }_{-\infty }e^{i \frac{p x_{o}}{\hslash }}|p\rangle _{1}|-p\rangle _{2}\textrm{d}p\) , where particles have opposite momenta, and \(\hslash =h/2\pi\) is the reduced Planck’s constant. Therefore, both position and momentum of each particle are completely unknown. If the position of any one particle is measured, then the EPR state is randomly collapsed onto \(|x'\rangle _{1}|x'+{\textbf {x}}_{o}\rangle _{2}\) where a prime on x indicates a single measured position value from the integral range. Therefore, the measured positions of particles are correlated, i.e. they are separated by \({\textbf {x}}_{o}\) irrespective of \(x'\) . Instead of position, if momentum, which is a complementary observable to the position, of a particle is measured, then the EPR state is randomly collapsed onto \(| p'\rangle _{1}|-p'\rangle _{2}\) , where both the particles exhibit opposite momenta irrespective of \(p'\) thus, their measured momenta are correlated.

A schematic diagram of the experiment, where a screen corresponds to a single photon detector capable of detecting locations of photon detection events. A screen is placed considerably closer to the source than a beam splitter and a double-slit.

In this paper, the EPR state of two photons in three-dimensions, propagated away from a finite size of source, is evaluated as follows: Consider a schematic of the experiment shown in Fig.  1 , where EPR entangled photons are produced by a finite source size. Photon-1 is detected on a screen, which can record the position of a detected photon as a point on the screen. This measurement corresponds to a position measurement of photon-1 while photon-2 is propagating towards a double-slit, and later it passes through a 50:50 beam splitter. The reflected probability amplitude of photon-2 is incident on a single photon detector-3, which is placed at the focal point of a convex lens. Whereas the transmitted probability amplitude is passed through a double-slit and incident on a single photon detector-2. The detector-2 is stationary, and it measures the position of photon-2 behind the double-slit. Each single photon detector is equipped with a very narrow aperture in order to measure the position of a photon around a location.

To evaluate the EPR state of two photons emanating from a three-dimensional source of finite extension, consider a source placed around the origin of a right-handed Cartesian coordinate system, as shown in Fig.  1 . Two photons are produced simultaneously from each point in the source as a consequence of the EPR constraint. Corresponding to an arbitrary point \(\mathbf {r'}\) within the source, a two-photon probability amplitude to find photon-1 at a point \(o_{a}\) in region- a left to the source and photon-2 at a point \(o_{b}\) in region- b right to the source is written as \(\frac{e^{ip_{1}|\textbf{r}_{a}-\textbf{r}'|/\hslash }}{|\textbf{r}_{a}-\textbf{r}'|}\frac{e^{ip_{2}|\textbf{r}_{b}-\textbf{r}'|/\hslash }}{|\textbf{r}_{b}-\textbf{r}'|}\) 38 , 39 , where \(p_{1}\) and \(p_{2}\) are magnitudes of momentum of photon-1 and of photon-2, respectively, and \(\textbf{r}_{a}\) and \(\textbf{r}_{b}\) are the position vectors of points \(o_{a}\) and \(o_{b}\) from the origin. Since the source size is finite, the total finite amplitude to find a photon at \(o_{a}\) and a photon at \(o_{b}\) is a linear quantum superposition of amplitudes originating from all points located in the source, which is written as

where both photons have the same linear polarisation state. A case for different polarisation states of photons leads to a hyper-entangled state, which is reported in Refs. 40 , 41 . However, for this experiment, an EPR entanglement is sufficient. Therefore, both photons are assumed to have the same linear polarisation state along the y -axis, which is omitted in this analysis. In Eq. ( 1 ), \(A_{o}\) is a constant, and \(\psi (x',y',z')\) is the probability amplitude of a pair production at a position \(r'(x',y',z')\) in the source. This amplitude is constant for an infinitely extended EPR state at any arbitrary position vector \(\textbf{r}'\) in the source. This integral represents the amplitude of two photons emanating from a three-dimensional photon pair source of finite size. It leads to a two-photon amplitude, which corresponds to the probability amplitude to find two photons together at different locations. Further, the magnitudes of momenta of photons are considered to be equal \(p_{1}=p_{2}=p\) , for the degenerate photon pair production. The amplitude of pair production \(\psi (x',y',z')\) is considered to be a three-dimensional Gaussian function such that, \(\psi (x',y',z')= a e^{-(x'^2+y'^2)/\sigma ^2}e^{-z'^2/w^2}\) , where a is a constant, \(\sigma\) and w are the widths of the Gaussian.

To evaluate the integral, consider two planes oriented perpendicular to the z -axis such that a plane-1 is located at a distance \(s_{1}\) and a plane-2 is located at a distance \(s_{2}\) from the origin. These planes are not shown in Fig.  1 however, a screen can be placed in a plane-1 and a double-slit can be placed in a plane-2. The amplitude to find photon-1 on plane-1 and photon-2 on plane-2 is evaluated as follows: Consider the distances of planes from the origin are such that, \(\sigma ^{2}p/h s_{1}\ge 1\) and \(\sigma ^{2}p/h s_{2} \ge 1\) , where the magnitudes of \(s_{1}\) and \(s_{2}\) are considerably larger than \(\sigma\) and w . This approximation is valid for the experimental considerations of this paper. Since the double-slit and the detectors are placed close to the z -axis therefore, Eq. ( 1 ) can be written as

where \(\Phi (x_{1},y_{1}; x_{2}, y_{2})\) is a two-photon position amplitude with variables of its argument separated by a semicolon denoting a position of photon-1 on plane-1 and of photon-2 on plane-2. After solving the integral, \(\Phi (x_{1},y_{1}; x_{2}, y_{2})\) is written as

where \(c_{n}\) is a constant and tan( \(\Phi\) )=–p(s 1 +s 2 )σ 2 /2 ℏ s 1 s 2 . It is evident from Eq. ( 3 ) that both photons can be found at arbitrary positions. Once a photon is detected at a well-defined location ( \(x'_{i}, y'_{i}\) ), where a label \(i\in \{1,2\}\) corresponds to any single measured photon, then its position is determined. This measurement collapses the total wavefunction of both photons. Note that when a photon is detected at a well-defined position, even then the amplitude to find the other photon in the position space is delocalised, i.e. the projected position wavefunction has a nonzero spread. This wavefunction projection happens immediately once a photon is detected.

The second order quantum interference is exhibited if photon-1 detections are retained on the screen with the condition that photon-2 is detected after the double-slit by a stationary detector-2 as shown in Fig.  1 . However, this stationary detector will not always detect photon-2 since, photon has a nonzero amplitude to exist at different positions even after passing through the double-slit. The conditional detection corresponds to a joint measurement of photons. If all photon-1 detections on the screen are considered, then the interference pattern does not appear. Single photon interference is suppressed on the screen as well as after the double-slit, since photons are EPR entangled. To evaluate the second order interference pattern, consider a screen placed at \(z=-s_{1}\) and a double-slit placed at \(z=s_{2}\) with their planes oriented perpendicular to the z -axis. If the transmission function of the double-slit is \(A_{T}(x_{2},y_{2})\) then the joint amplitude to detect photon-1 on the screen at a position \((x_{1}, y_{1})\) and photon-2 by a stationary detector-2 is written as

where an integration represents a projection onto a quantum superposition of position states of the photon-2 in the plane of the double-slit. A phase multiplier \(B(x_{2}, y_{2})=e^{ipr_{d}/\hslash }\) represents a phase acquired by a photon to reach detector-2 from the double-slit plane. The distance between detector-2 location ( \(x_{o}, y_{o}, z_{o}\) ) and an arbitrary point location ( \(x_{2}, y_{2}, s_{2}\) ) in the double-slit plane is \(r_{d}=(D^{2}+(x_{2}-x_{o})^{2}+ (y_{2}-y_{o})^{2})^{1/2}\) , where \(D=z_{o}-s_{2}\) is the distance of detector-2 from the double-slit. Note that \(x_{o}\) is different than the symbol \({\textbf {x}}_{o}\) which is denoting separation of particles in the one-dimensional EPR state. Thus, the second order interference pattern depends on the position of detector-2. For a double-slit with slit separation d along the x -axis and infinite extension along the y -axis, the transmission function is given by \(A_{T}(x_{2},y_{2})= [\delta (x_{2}-d/2)+\delta (x_{2}+d/2)]/\sqrt{2}\) . In the following experiment, each slit of the double-slit is largely extended along the y -axis as compared to its width. The effect of slit width and position resolution of single photon detectors is considered in the analysis of the following experiment. It is also evident that the two-photon interference pattern exhibits a shift when the position of the stationary detector-2 is shifted.

Experimental results

An experiment is performed with continuous variable EPR entangled photons of equal wavelength 810 nm, which are produced by the Type-I SPDC in a negative-uniaxial BBO nonlinear crystal. An experimental diagram of the setup is shown in Fig.  2 , where the x -axis is perpendicular to the optical table passing through the crystal. This experimental setup is a folded version of a diagram shown in Fig.  1 , where folding is along the x -axis such that photons propagate close to the angle of the conical emission pattern in a horizontal plane parallel to the optical table. Furthermore, photons propagating at a small inclination w.r.t. a horizontal plane pass through the double-slit. A vertical linearly polarised laser beam, along the x -axis, of wavelength 405 nm is expanded ten times to obtain a beam diameter of 8 mm at the full-width-half-maximum. The expanded laser beam is passed through the BBO crystal, whose optic-axis can be precisely tilted in a vertical plane passing through the crystal. This configuration results in noncollinear spontaneous down-converted photon pair emission in a broad conical pattern, where both the photons of each pair have the same linear polarisation state perpendicular to the polarisation state of the pump photons. The down-converted photons are EPR entangled in a plane perpendicular to the symmetry axis of the cone. The pump laser beam, after passing through the nonlinear crystal, is absorbed by a beam dumper to minimise unwanted background light.

An experimental diagram, where EPR entangled pairs of photons are emanated in a conical emission pattern. The paths of entangled photons are represented by red lines. The pump laser beam, after passing through the crystal, is represented by a narrow white line for clarity. The x -axis is perpendicular to the optical table and passing though the nonlinear crystal.

A screen is represented by a movable single photon detector-1 ( \(D_{1}\) ), which is placed close to the crystal at a distance of 26.4 cm to detect photon-1 at about 5.68 ns prior to the detection of photon-2. The aperture of a single photon detector \(D_{1}\) is an elongated single-slit of width 0.1 mm along the x -axis, which represents an effective detector width. It also corresponds to the resolution of the position measurements along the x -axis. This detector can be displaced parallel to the x -axis in steps of 0.1 mm to detect photons at different positions. Photon-1 is passed through a band-pass filter of band-width 10 nm at the centre wavelength 810 nm prior to its detection. Photon-2 is incident on a 50:50 polarisation independent beam splitter, which is placed at a distance of 93.8 cm from the crystal. A double-slit with an orientation of single slits perpendicular to the x -axis is placed after the beam splitter at a distance of 3 cm. Another elongated single-slit aperture of width 0.1 mm along the x -axis is placed after the double-slit at a distance of 23 cm from the double-slit in front of an optical fibre coupler. After passing through the double-slit, photon-2 is filtered by a band-pass filter of band-width 10 nm at the centre wavelength 810 nm. It is then passed through the aperture and directed towards a single photon detector-2 ( \(D_{2}\) ) with a multimode optical fibre of length 0.5 m. This single-slit aperture can be displaced along the x -axis with a resolution of 0.1 mm. However, it is positioned at a predetermined location during one complete interference pattern data collection. In this experimental configuration, photon-1 is detected much earlier while photon-2 is propagating towards the beam splitter. Detection of photon-1 cannot affect photon-2 through any signalling limited by the speed of light until it reaches at an optical fibre coupler placed after the double-slit. Photon-2 arrives at the beam splitter 2.26 ns after the detection of photon-1, and from the beam splitter, its transmitted amplitude takes about 0.1 ns to arrive at the double-slit. The reflected amplitude of photon-2 is detected after passing through a band-pass filter by another optical fibre coupled single photon detector-3 ( \(D_{3}\) ) without any aperture. Photons are focused on an optical fibre input with a convex lens, which projects the incident quantum state of photon-2 onto an eigen-state of the transverse momentum, provided photon-2 is detected by a single photon detector \(D_{3}\) . Distance of the lens from the beam splitter is 25 cm, where this lens and the single photon detector \(D_{3}\) are positioned at predetermined fixed locations throughout the experiment.

( a ) Quantum interference pattern obtained by measuring the coincidence detection of photons by a variable position single photon detector \(D_{1}\) and a stationary single photon detector \(D_{2}\) , where a solid line represents the theoretically evaluated interference pattern. ( b ) Coincidence detection of photons results in no interference, when photon-2 is detected by a stationary single photon detector \(D_{3}\) and photon-1 is detected by \(D_{1}\) . Each data point is an average of ten repetitions of the experiment with 60 s time of exposure.

The shift in the two-photon quantum interference pattern when, ( a ) single photon detector \(D_{2}\) position is \(x_{o} = +0.11\) mm, ( b ) \(D_{2}\) position is \(x_{o} = -0.11\) mm. Single photons do not interfere in this experiment. Each data point is an average of ten repetitions of the experiment with 60 s time of exposure.

The experiment is performed with 19 mW power of the pump laser beam, which is incident on the crystal. Each single photon detector output is connected to an electronic time correlated single photon counter (TCSPC), which measures the single and coincidence photon counts with 81 ps temporal resolution. A selected width of time window for the coincidence detection of photons is 81 ns. Single photon counts of each detector and coincidence photon counts of \(D_{1}\) and \(D_{2}\) , \(D_{1}\) and \(D_{3}\) are measured for 60 s. These measurements are repeated ten times to obtain an average of photon counts. A two-photon quantum interference pattern with a reversible detection of photons is shown in Fig.  3 a, where open circles represent the measured coincidence photon counts of single photon detectors \(D_{1}\) and \(D_{2}\) and the single photon counts of \(D_{1}\) . Whereas, a solid line corresponds to the theoretical calculation of two-photon quantum interference using Eq. ( 4 ) by considering the finite width of each slit of the double-slit and position resolution of \(D_{2}\) . A position of \(D_{2}\) relative to the double slit is \((x_{o}, D)\) in a vertical plane with \(D=23\) cm. The two-photon quantum interference pattern exhibits a shift as the position \(x_{o}\) of \(D_{2}\) is displaced, which is due to the phase-shift multiplier term \(B(x_{2}, y_{2})=e^{ipr_{d}/\hslash }\) in Eq. ( 4 ). The slit separation of the double-slit is 0.75 mm and the width of each slit is 0.15 mm. A fixed position of a single photon detector \(D_{2}\) is taken to be the reference point with \(x_{o}=0\) . There is no single photon interference pattern produced in this experiment by scanning the detector \(D_{1}\) or \(D_{2}\) . When photon-1 is detected, photon-2 is still propagating towards the beam splitter, and later its transmitted amplitude is detected by a fixed position single photon detector \(D_{2}\) at a time lapse of 5.68 ns after the detection of a photon-1. On the other hand, if the reflected amplitude of photon-2 is detected by a single photon detector \(D_{3}\) then \(D_{2}\) will not measure any photon. In this case, photon-2 is not passed through the double-slit, and therefore, no two-photon quantum interference results as shown in Fig.  3 b, which shows coincidence counts of single photon detectors \(D_{1}\) and \(D_{3}\) and the single counts of \(D_{1}\) . A choice of whether to detect a photon after the double-slit or not is naturally and randomly occurring due to the presence of a beam splitter in the path of photon-2 after its detection. A path superposition quantum state of photon-2 after the beam splitter is projected either onto the transmitted or the reflected path due to a single photon detection by a detector \(D_{2}\) or \(D_{3}\) , respectively. The main characteristic of two-photon quantum interference is that it exhibits a shift of the entire pattern as the single photon detector \(D_{2}\) is displaced to another fixed position. This shift in the pattern is shown in Fig.  4 when, (a) \(D_{2}\) is placed at a position \(x_{o}= 0.11\) mm, (b) \(D_{2}\) is placed at a position \(x_{o}=-0.11\) mm with same D . This shift is also observed experimentally in the quantum ghost interference experiment by Strekalov et al. 23 . As a consequence of the EPR entanglement, there is no single photon interference. Therefore, the experiment in this paper presents a quantum two-photon interference with a reversible detection of photons, which has no classical counterpart.

This paper presents a two-photon double-slit experiment with the reversible detection of photons. Continuous variable EPR entangled photons are produced by the Type-I SPDC process, where photon-1 is detected on a screen while photon-2 is propagating towards a beam splitter. At a later time, photon-2 is produced in a quantum superposition of reflected and transmitted path amplitudes at the beam splitter. The transmitted amplitude is passed through the double-slit, and if this amplitude is detected by a detector-2 then the path quantum superposition state of photon-2 is collapsed onto the transmitted path. Then detector-3 does not detect this photon. Since photon-2 interacted with the double-slit considerably later than the detection of photon-1 therefore, it is ruled out that photon-1 has carried the path information of photon-2 in the double-slit to suppress the single photon interference. In addition, a position measurement of photon-1 cannot affect photon-2 through any signal propagating with speed, which is limited by the speed of light. If photon-2 is detected by a detector-3 then the quantum superposition state is collapsed onto the reflected path. Therefore, detector-2 does not detect photon-2, which results in no interference in single photon and two-photon measurements.

It is very important to expand the beam diameter of the pump laser beam to produce a continuous variable EPR quantum entangled state. It also leads to a broader envelope of the interference pattern. To achieve low background counts limited by the dark counts of the single photon detectors, the pump laser beam should have minimal scattering from optical components, and it should be properly dumped after passing through the crystal. A source of EPR entangled photons consists of a thin crystal in Type-1 SPDC configuration, where down-converted photons have the same linear polarisation. The nonlinear crystal is anti-reflection coated for wavelengths of pump and down-converted photons to reduce scattering and back reflection. The nonlinear crystal is kept at room temperature without any temperature control. Its optical-axis is precisely aligned w.r.t. the polarisation vector of the pump laser beam to obtain a broad conical emission pattern of down-converted photons with a full cone angle of  9.5°. The optical power of the pump laser beam is 19 mW, which is x -polarised. Single-slit apertures, which are placed in front of \(D_{1}\) and an input coupler of an optical fibre of \(D_{2}\) , are attached to translational stages to displace them precisely to collect photons corresponding to different positions of apertures. To increase the number of photons passing through the double slit, a double slit consists of two elongated single slits separated by a distance of 0.75 mm along the x -axis, where the width of each slit is 0.15 mm. In the experimental configuration, photons are EPR entangled in a plane perpendicular to the direction of propagation of the pump laser beam. The efficiency of each single photon detector is about 65 %. The single photon detector \(D_{1}\) equipped with a convex lens is directly collecting photons and it is placed close to the crystal. Whereas, the single photon detectors \(D_{2}\) and \(D_{3}\) are coupled to multimode optical fibres of length 0.5 m. The input of each optical fibre is attached to respective optical fibre couplers, each consisting of a convex lens of diameter  1 cm. Photons are collected by the lenses after passing through the single-slit apertures to measure the position of photons by \(D_{1}\) and \(D_{2}\) . However, a coupler of a single photon detector \(D_{3}\) is not equipped with any aperture. A band-pass optical filter of band-width 10 nm at centre wavelength  810 nm is placed at the input of each single photon detector to filter the unwanted scattered photons of the pump laser and background light.

Data availability

All data generated or analysed during this study are included in this article.

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Saxena, A., Kaur, M., Devrari, V. & Singh, M. Quantum ghost imaging of a transparent polarisation sensitive phase pattern. Sci. Rep. 12 , 21105 (2022).

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Acknowledgements

Mandip Singh acknowledges research funding by the Department of Science and Technology, Quantum Enabled Science and Technology grant for project No. Q.101 of theme title “Quantum Information Technologies with Photonic Devices”, DST/ICPS/QuST/Theme-1/2019 (General).

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MS setup the experiment and made its theoretical model, VD took data and analysed data, MS wrote this manuscript. Both authors discussed the experiment.

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Devrari, V., Singh, M. Quantum double slit experiment with reversible detection of photons. Sci Rep 14 , 20438 (2024). https://doi.org/10.1038/s41598-024-71091-1

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Researchers Achieve Fast Photon-Mediated Entanglement to Advance Quantum Technologies

• Research , Uncategorized

Matt Swayne

September 4, 2024.

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Insider Brief

• Researchers achieved fast photon-mediated entanglement between barium ions, boosting entanglement rates by more than a third using ytterbium ions for continuous cooling.
• The introduction of a co-trapped ytterbium ion for sympathetic cooling eliminated the need for recooling interruptions, significantly boosting entanglement success rates.
• This work demonstrates a scalable method for linking quantum computing nodes, paving the way for large-scale quantum networks and enhancing quantum computing, communication, and sensing technologies.

A team of scientists demonstrated fast photon-mediated entanglement between trapped ions, an advance that the team reports is a major step forward in quantum networking, among other quantum technologies.

The experiment, led by the Duke Quantum Center, achieved a record in entanglement rates between two barium ions while employing ytterbium ions for continuous sympathetic cooling. The results, published in Physical Review Letters and an earlier version on ArXiv , suggest promising advances toward scalable quantum networks, which are critical for the future of not justquantum computing, but also communication and sensing.

Quantum Networking with Trapped Ions Background

Trapped ions are one of the promising candidates for quantum networking and computing. Their natural homogeneity and isolation from environmental noise — the arch enemy of quantum calculations — make them ideal qubits, capable of maintaining coherence for long periods. However, establishing entanglement between distant trapped ions — a fundamental requirement for distributed quantum networks — has remained a technical challenge due to the probabilistic nature of photon emission and detection.

In this experiment, the research team used two co-trapped barium ions, entangling them by interfering single photons emitted by each ion. The researchers used special lenses — called 0.8 numerical aperture objectives — to capture the tiny particles of light that were emitted by the ions. These photons were then combined and mixed through a fiber optic splitter, a device that helps them interfere with each other. This interference caused the two ions to become “entangled,” meaning their states became linked, so that what happens to one can probabilistically affect the other, even if they’re far apart, which is referred to as an entangled Bell state.

The entanglement fidelity exceeded 94%, setting a high benchmark for photon-mediated ion entanglement.

The team writes that the use of photon-based interconnects is essential for linking quantum computing nodes, a task that would be exceedingly difficult with more conventional methods.

“Photonic interconnects between quantum processing nodes may be the only way to achieve large-scale quantum computers,” the researchers wrote in the paper.

Continuous Cooling with Ytterbium Ions

One of the key innovations in this experiment was the use of an additional ytterbium ion for continuous sympathetic cooling. This allowed the barium ions to remain cold and stable during extended periods of entanglement generation, eliminating the need for periodic recooling interruptions, which can significantly reduce entanglement rates.

In previous experiments, ions had to be recaptured and recooled after a limited number of entanglement attempts due to the heating effects of photon recoil, which is slight heating caused by tiny pushes or jolts that atoms or ions feel when they emit or absorb particles of light. This led to time-consuming delays and lower success rates. By continuously cooling the ions with a co-trapped ytterbium ion, the Duke team was able to achieve a continuous entanglement attempt rate of 1 MHz and a sustained ion-ion entanglement rate of 250 entangled states per second. This represents a substantial improvement of about 37% over previous records, where entanglement rates had been limited to about 182 entanglements per second.

The use of ytterbium ions as sympathetic coolants addresses the issue of heating without directly interfering with the barium ions’ quantum state preparation or detection. This work provides a new path to more efficient quantum networking operations.

Photon-Mediated Entanglement Process

The researchers detailed the process, adding it begins by preparing the two barium ions in a specific quantum state using a combination of optical pumping and laser excitation. When the ions return to their ground state, they emit single photons, which are collected through high-precision optics and routed to a Bell-state analyzer. If the photons interfere in the correct manner, the ions are projected into an entangled state.

In this experiment, the team achieved a photon-mediated entanglement success rate of 2.4 × 10⁻⁴ per attempt — or about 1 out of every 4,000 tries — a figure that could be further improved by upgrading to faster control systems.

According to the researchers, the experiment’s fidelity and success rate are largely attributed to the use of the 0.8 NA objectives, which increased the photon collection efficiency to 23%, much higher than previous experiments using 0.6 NA objectives. These improvements would be important in addressing the inefficiencies typically associated with photon-mediated entanglement.

Toward Scalable Quantum Networks

The team’s findings point to a promising future for scalable quantum networks. One of the biggest challenges in building large-scale quantum systems is connecting distant qubits with high fidelity and at practical speeds. Photon-mediated entanglement is a leading solution to this problem, and the Duke team’s experiment may being the field one step closer to practical implementations.

By reducing inefficiencies in photon collection and introducing sympathetic cooling to eliminate time-wasting recooling cycles, the team demonstrated a substantial increase in entanglement rates. This could, for example, pave the way for linking multiple quantum nodes over long distances, a necessary step toward the development of large-scale quantum computers and communication networks.

In practical terms, photon-mediated entanglement allows for the distribution of entangled states between quantum nodes without the need for physically moving qubits. This not only reduces latency but also increases the scalability of quantum systems. The researchers cited prior work that suggested such photon-based interconnects would be necessary for achieving the full potential of quantum computing, enabling control over larger quantum systems and greatly increasing computational power.

Broad Implications for Quantum Technologies

The implications of this work extend beyond quantum computing. As the researchers write in the paper, “Interconnects between quantum memories, even without multi-qubit universal control, offer diverse opportunities in quantum sensing, communication, and simulation.”

It’s possible this work could inform post-quantum encryption techniques. For example, the ability to generate high-fidelity entanglement at high rates is a significant advance for applications such as quantum key distribution, where secure communication relies on entangled quantum states.

In the field of quantum sensing, networks of entangled quantum sensors could provide unprecedented precision in measurements, enabling advances in fields ranging from gravitational wave detection to materials science.

For quantum simulation, where researchers aim to model complex quantum systems that are otherwise too difficult to study with classical computers, the ability to entangle remote qubits could enable simulations of larger and more intricate systems.

Limitations and Future Directions

Despite the success of this experiment, the researchers acknowledge that further improvements are necessary before photon-mediated entanglement can be widely deployed in practical quantum networks. One area of focus is increasing the photon collection efficiency even further, potentially through the use of optical cavities or integrated photonic systems.

Another promising direction is the use of alternative ion species with higher photon emission rates. The team also noted that using faster control electronics could significantly reduce latency, further boosting the rate of successful entanglement events.

In the long term, building a network of quantum nodes that can exchange entangled states across long distances will require integrating these techniques into larger, more complex systems. The Duke team’s work represents an important step in that direction, providing key insights into the challenges and opportunities of building these scalable quantum networks.

The continued development of quantum networking technologies, such as those demonstrated in this experiment, could ultimately lead to the realization of the long-envisioned quantum internet, where information is transmitted securely and efficiently using the principles of quantum mechanics.

The study was conducted by Jameson O’Reilly, George Toh, Isabella Goetting, Sagnik Saha, Mikhail Shalaev, Ashish Kalakuntla, Tingguang Li, Ashrit Verma, and Christopher Monroe from the Duke Quantum Center, Departments of Electrical and Computer Engineering and Physics, Duke University. Allison Carter and Andrew Risinger, formerly of Duke, are now affiliated with the National Institute of Standards and Technology and Intel Corp., respectively. The team also included researchers from the Joint Quantum Institute at the University of Maryland, College Park.

For a deeper dive into the technical aspects of the research that this summary might not provide, read the paper on Physical Review Letters . Also, important to note, for access, I used the ArXiv paper , which may not be completely updated.

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'Unbreakable' quantum communication closer to reality thanks to new, exceptionally bright photons

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Scientists have created an "exceptionally bright" light source that can generate quantum-entangled photons (particles of light) which could be used to securely transmit data in a future high-speed quantum communications network.

A future quantum internet could transmit information using pairs of entangled photons — meaning the particles share information over time and space regardless of distance. Based on the weird laws of quantum mechanics , information encoded into these entangled photons can be transferred at high speeds while their "quantum coherence" — a state in which the particles are entangled — ensures the data cannot be intercepted.

But one of the key challenges in building a quantum internet has been that the strength of these photons can fade the further they travel; the light sources have not been bright enough. To build a successful quantum internet that can send data over vast distances, photons must be strong enough to prevent "decoherence" — where entanglement is lost and the information they contain disappears.

In research published 24 July in the journal eLight , scientists from Europe, Asia and South America created a new type of quantum signal source using existing technologies that achieves extremely high brightness.

Related: Quantum data beamed alongside 'classical data' in the same fiber-optic connection for the 1st time

They achieved this by combining a photon dot emitter (a generator of single photons, or a particle of light) with a quantum resonator (a device to strengthen the quantum signature) to create the powerful new quantum signal.

What makes the recent research especially interesting is that the individual technologies have been independently proven in laboratories, but they had only been tested separately. This study is the first time they have been used in conjunction with each other.

Researchers combined the photon dot emitter with a circular Bragg resonator (a reflector used to guide electromagnetic waves) on a piezoelectric actuator (a device that generates electricity when heat or stress is applied). Together they created an enhanced form of photon emitter, which can fine-tune the emitted photons for maximum polarized entanglement. This was controlled by using the piezoelectric actuator.

Photon pairs generated by the device had a high entanglement fidelity and extraction efficiency — meaning that each photon is bright enough to be useful and holds its "quantum signature" (a useful quantum property) well. It was previously hard to achieve both a useful level of brightness and a high entanglement fidelity at the same time, because each aspect required a different technology and these were difficult to combine in a scalable manner.

This is a significant step forward in developing practical quantum technologies, demonstrating how they can be combined together to create a more powerful and viable light source.

Unfortunately, we should not expect a quantum internet any time soon, as the various technologies remain in the experimental and development phase. Making the photon emitter used in the study also required toxic raw materials, including arsenic, which required specialist handling. There are also safety concerns around the use of gallium arsenide, which the photon dot emitter was made from. Fisher Scientific , a supplier of laboratory equipment and chemicals for scientific research, lists gallium arsenide as hazardous for several reasons, including its carcinogenic properties.

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The safety concerns relating to the use of these materials could limit the scalability of the methodology outlined. Viable alternative materials may therefore need to be identified in generating bright, entangled photons for future quantum communications network

The next stage in the development process will be to integrate a diode-like structure onto the piezoelectric actuator. This would allow an electric field to be generated across the quantum dots, in order to counteract decoherence and therefore boost the degree of entanglement.

Although there are many further steps to take in developing a quantum internet, successfully combining a photon emitter and a resonator to achieve photons with high brightness and entanglement is nonetheless a significant step forward, the scientists said.

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Title: experimental measurement and a physical interpretation of quantum shadow enumerators.

Abstract: Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators.

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