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

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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## How Bell’s Theorem Proved ‘Spooky Action at a Distance’ Is Real

July 20, 2021

Samuel Velasco/Quanta Magazine

## Introduction

We take for granted that an event in one part of the world cannot instantly affect what happens far away. This principle, which physicists call locality, was long regarded as a bedrock assumption about the laws of physics. So when Albert Einstein and two colleagues showed in 1935 that quantum mechanics permits “spooky action at a distance,” as Einstein put it, this feature of the theory seemed highly suspect. Physicists wondered whether quantum mechanics was missing something.

Then in 1964, with the stroke of a pen, the Northern Irish physicist John Stewart Bell demoted locality from a cherished principle to a testable hypothesis. Bell proved that quantum mechanics predicted stronger statistical correlations in the outcomes of certain far-apart measurements than any local theory possibly could. In the years since, experiments have vindicated quantum mechanics again and again.

Bell’s theorem upended one of our most deeply held intuitions about physics, and prompted physicists to explore how quantum mechanics might enable tasks unimaginable in a classical world. “The quantum revolution that’s happening now, and all these quantum technologies — that’s 100% thanks to Bell’s theorem,” says Krister Shalm , a quantum physicist at the National Institute of Standards and Technology.

Here’s how Bell’s theorem showed that “spooky action at a distance” is real.

## Ups and Downs

The “spooky action” that bothered Einstein involves a quantum phenomenon known as entanglement, in which two particles that we would normally think of as distinct entities lose their independence. Famously, in quantum mechanics a particle’s location, polarization and other properties can be indefinite until the moment they are measured. Yet measuring the properties of entangled particles yields results that are strongly correlated, even when the particles are far apart and measured nearly simultaneously. The unpredictable outcome of one measurement appears to instantly affect the outcome of the other, regardless of the distance between them — a gross violation of locality.

To understand entanglement more precisely, consider a property of electrons and most other quantum particles called spin. Particles with spin behave somewhat like tiny magnets. When, for instance, an electron passes through a magnetic field created by a pair of north and south magnetic poles, it gets deflected by a fixed amount toward one pole or the other. This shows that the electron’s spin is a quantity that can have only one of two values: “up” for an electron deflected toward the north pole, and “down” for an electron deflected toward the south pole.

Imagine an electron passing through a region with the north pole directly above it and the south pole directly below. Measuring its deflection will reveal whether the electron’s spin is “up” or “down” along the vertical axis. Now rotate the axis between the magnet poles away from vertical, and measure deflection along this new axis. Again, the electron will always deflect by the same amount toward one of the poles. You’ll always measure a binary spin value — either up or down — along any axis.

It turns out it’s not possible to build any detector that can measure a particle’s spin along multiple axes at the same time. Quantum theory asserts that this property of spin detectors is actually a property of spin itself: If an electron has a definite spin along one axis, its spin along any other axis is undefined.

## Local Hidden Variables

Armed with this understanding of spin, we can devise a thought experiment that we can use to prove Bell’s theorem. Consider a specific example of an entangled state: a pair of electrons whose total spin is zero, meaning measurements of their spins along any given axis will always yield opposite results. What’s remarkable about this entangled state is that, although the total spin has this definite value along all axes, each electron’s individual spin is indefinite.

Suppose these entangled electrons are separated and transported to distant laboratories, and that teams of scientists in these labs can rotate the magnets of their respective detectors any way they like when performing spin measurements.

When both teams measure along the same axis, they obtain opposite results 100% of the time. But is this evidence of nonlocality? Not necessarily.

Alternatively, Einstein proposed, each pair of electrons could come with an associated set of “hidden variables” specifying the particles’ spins along all axes simultaneously. These hidden variables are absent from the quantum description of the entangled state, but quantum mechanics may not be telling the whole story.

Hidden variable theories can explain why same-axis measurements always yield opposite results without any violation of locality: A measurement of one electron doesn’t affect the other but merely reveals the preexisting value of a hidden variable.

Bell proved that you could rule out local hidden variable theories, and indeed rule out locality altogether, by measuring entangled particles’ spins along different axes.

Suppose, for starters, that one team of scientists happens to rotate its detector relative to the other lab’s by 180 degrees. This is equivalent to swapping its north and south poles, so an “up” result for one electron would never be accompanied by a “down” result for the other. The scientists could also choose to rotate it an in-between amount — 60 degrees, say. Depending on the relative orientation of the magnets in the two labs, the probability of opposite results can range anywhere between 0% and 100%.

Without specifying any particular orientations, suppose that the two teams agree on a set of three possible measurement axes, which we can label A, B and C. For every electron pair, each lab measures the spin of one of the electrons along one of these three axes chosen at random.

Let’s now assume the world is described by a local hidden variable theory, rather than quantum mechanics. In that case, each electron has its own spin value in each of the three directions. That leads to eight possible sets of values for the hidden variables, which we can label in the following way:

The set of spin values labeled 5, for instance, dictates that the result of a measurement along axis A in the first lab will be “up,” while measurements along axes B and C will be “down”; the second electron’s spin values will be opposite.

For any electron pair possessing spin values labeled 1 or 8, measurements in the two labs will always yield opposite results, regardless of which axes the scientists choose to measure along. The other six sets of spin values all yield opposite results in 33% of different-axis measurements. (For instance, for the spin values labeled 5, the labs will obtain opposite results when one measures along axis B while the other measures along C; this represents one-third of the possible choices.)

Thus the labs will obtain opposite results when measuring along different axes at least 33% of the time; equivalently, they will obtain the same result at most 67% of the time. This result — an upper bound on the correlations allowed by local hidden variable theories — is the inequality at the heart of Bell’s theorem.

## Above the Bound

Now, what about quantum mechanics? We’re interested in the probability of both labs obtaining the same result when measuring the electrons’ spins along different axes. The equations of quantum theory provide a formula for this probability as a function of the angles between the measurement axes.

According to the formula, when the three axes are all as far apart as possible — that is, all 120 degrees apart, as in the Mercedes logo — both labs will obtain the same result 75% of the time. This exceeds Bell’s upper bound of 67%.

That’s the essence of Bell’s theorem: If locality holds and a measurement of one particle cannot instantly affect the outcome of another measurement far away, then the results in a certain experimental setup can be no more than 67% correlated. If, on the other hand, the fates of entangled particles are inextricably linked even across vast distances, as in quantum mechanics, the results of certain measurements will exhibit stronger correlations.

Since the 1970s, physicists have made increasingly precise experimental tests of Bell’s theorem. Each one has confirmed the strong correlations of quantum mechanics. In the past five years, various loopholes have been closed. Physicists continue to grapple with the implications of Bell’s theorem, but the standard takeaway is that locality — that long-held assumption about physical law — is not a feature of our world.

Editor’s note: The author is currently a postdoctoral researcher at JILA in Boulder, Colorado.

Clarification August 19, 2021: This article was revised to remove the impression that the standard interpretation of Bell’s theorem is universally accepted among physicists.

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https://www.nist.gov/news-events/news/2015/11/nist-team-proves-spooky-action-distance-really-real

## NIST Team Proves 'Spooky Action at a Distance' is Really Real

NIST physicist Krister Shalm with the photon source used in the Bell test that strongly supported a key prediction of quantum mechanics: There are in fact spooky actions at a distance.

BOULDER, Colo.—Einstein was wrong about at least one thing: There are, in fact, "spooky actions at a distance," as now proven by researchers at the National Institute of Standards and Technology (NIST).

Einstein used that term to refer to quantum mechanics, which describes the curious behavior of the smallest particles of matter and light. He was referring, specifically, to entanglement, the idea that two physically separated particles can have correlated properties, with values that are uncertain until they are measured. Einstein was dubious, and until now, researchers have been unable to support it with near-total confidence.

As described in a paper posted online and published in Physical Review Letters ( PRL ) ,* researchers from NIST and several other institutions created pairs of identical light particles, or photons, and sent them to two different locations to be measured. Researchers showed the measured results not only were correlated, but also—by eliminating all other known options—that these correlations cannot be caused by the locally controlled, "realistic" universe Einstein thought we lived in. This implies a different explanation such as entanglement.

The NIST experiments are called Bell tests, so named because in 1964 Irish physicist John Bell showed there are limits to measurement correlations that can be ascribed to local, pre-existing (i.e. realistic) conditions. Additional correlations beyond those limits would require either sending signals faster than the speed of light, which scientists consider impossible, or another mechanism, such as quantum entanglement.

The research team achieved this feat by simultaneously closing all three major "loopholes" that have plagued previous Bell tests. Closing the loopholes was made possible by recent technical advances, including NIST's ultrafast single-photon detectors, which can accurately detect at least 90 percent of very weak signals, and new tools for randomly picking detector settings.

"You can't prove quantum mechanics, but local realism, or hidden local action, is incompatible with our experiment," NIST's Krister Shalm says. "Our results agree with what quantum mechanics predicts about the spooky actions shared by entangled particles."

The NIST paper was published by PRL with another paper by a team at the University of Vienna in Austria who used a similar high-efficiency single-photon detector provided by NIST to perform a Bell test that achieved similar results.

The NIST results are more definitive than those reported recently by researchers at Delft University of Technology in the Netherlands.

In the NIST experiment, the photon source and the two detectors were located in three different, widely separated rooms on the same floor in a large laboratory building. The two detectors are 184 meters apart, and 126 and 132 meters, respectively, from the photon source.

Photon pairs are then separated and sent by fiber-optic cable to separate detectors in the distant rooms. While the photons are in flight, a random number generator picks one of two polarization settings for each polarization analyzer. If the photon matched the analyzer setting, then it was detected more than 90 percent of the time.

In the best experimental run, both detectors simultaneously identified photons a total of 6,378 times over a period of 30 minutes. Other outcomes (such as just one detector firing) accounted for only 5,749 of the 12,127 total relevant events. Researchers calculated that the maximum chance of local realism producing these results is just 0.0000000059, or about 1 in 170 million. This outcome exceeds the particle physics community's requirement for a "5 sigma" result needed to declare something a discovery. The results strongly rule out local realistic theories, suggesting that the quantum mechanical explanation of entanglement is indeed the correct explanation.

The NIST experiment closed the three major loopholes as follows:

Fair sampling: Thanks to NIST's single-photon detectors, the experiment was efficient enough to ensure that the detected photons and measurement results were representative of the actual totals. The detectors, made of superconducting nanowires, were 90 percent efficient, and total system efficiency was about 75 percent.

No faster-than-light communication: The two detectors measured photons from the same pair a few hundreds of nanoseconds apart, finishing more than 40 nanoseconds before any light-speed communication could take place between the detectors. Information traveling at the speed of light would require 617 nanoseconds to travel between the detectors.

Freedom of choice: Detector settings were chosen by random number generators operating outside the light cone (i.e., possible influence) of the photon source, and thus, were free from manipulation. (In fact, the experiment demonstrated a "Bell violation machine" that NIST eventually plans to use to certify randomness .)

To further ensure that hidden variables such as power grid fluctuations could not have influenced the results, the researchers performed additional experimental runs mixed with another source of randomness—data from popular movies, television shows and the digits of Pi. This didn't change the outcome.

The experiment was conducted at NIST's Boulder, Colo., campus, where researchers made one of the photon detectors and provided theoretical support. Researchers at the Jet Propulsion Laboratory (Pasadena, Calif.) made the other detector. Researchers at NIST's Gaithersburg, Md., headquarters built random number generators and related circuits. Researchers from the University of Illinois (Urbana-Champaign, Ill.) and the University of Waterloo and University of Moncton in Canada helped develop the photon source and perform the experiments. Researchers at the Barcelona Institute of Science and Technology in Spain developed another random number generator.

Funding for NIST contributions to the experiment was provided, in part, by the Defense Advanced Research Projects Agency. As a non-regulatory agency of the U.S. Department of Commerce, NIST promotes U.S. innovation and industrial competitiveness by advancing measurement science, standards and technology in ways that enhance economic security and improve our quality of life. To learn more about NIST, visit www.nist.gov .

* L.K. Shalm, E. Meyer-Scott, B.G. Christensen, P. Bierhorst, M.A. Wayne, D.R. Hamel, M.J. Stevens, T. Gerrits, S. Glancy, M.S. Allman, K.J. Coakley, S.D. Dyer, C. Hodge, A.E. Lita, V.B. Verma, J.C. Bienfang, A.L. Migdall, Y. Zhang, W.H. Farr, F. Marsili, M.D. Shaw, J.A. Stern, C. Abellan, W. Amaya, V. Pruneri, T. Jennewein, M.W. Mitchell, P.G. Kwiat, R.P. Mirin, E. Knill and S.W. Nam. A strong loophole-free test of local realism. Physical Review Letters . December 16, 2015. DOI: 10.1103/PhysRevLett.115.250402.

Note: Release updated on Dec. 16, 2015, to note publication of the two PRL papers.

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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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A physicist explains the science of Einstein’s ‘spooky action at a distance’ Published: October 6, 2022 1.51pm EDT Associate Professor of Physics, University of South Florida English We...

The “spooky action” that bothered Einstein involves a quantum phenomenon known as entanglement, in which two particles that we would normally think of as distinct entities lose their independence. Famously, in quantum mechanics a particle’s location, polarization and other properties can be indefinite until the moment they are measured.

November 10, 2015 NIST physicist Krister Shalm with the photon source used in the Bell test that strongly supported a key prediction of quantum mechanics: There are in fact spooky actions at a distance. Credit: J. Burrus/NIST

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...

In physics, action at a distance is the concept that an object can be affected without being physically touched (as in mechanical contact) by another object. That is, it is the non-local interaction of objects that are separated in space. Non-contact forces is action at a distance affecting specifically an object's motion .