# Quantum Entanglement

Quantum entanglement is a bizarre, counterintuitive phenomenon that explains how two subatomic particles can be intimately linked to each other even if separated by billions of light-years of space. Despite their vast separation, a change induced in one will affect the other.

## Quantum Entanglement

In 1964, physicist John Bell posited that such changes can be induced and occur instantaneously, even if the particles are very far apart. Bell's Theorem is regarded as an important idea in modern physics, but it conflicts with other well-established principles of physics. For example, Albert Einstein (opens in new tab) had shown years before Bell proposed his theorem that information cannot travel faster than the speed of light (opens in new tab). Perplexed, Einstein famously described this entanglement phenomenon as "spooky action at a distance."

In late 2021, an international group of researchers reported they had successfully subjected a tardigrade to temporary quantum entanglement (opens in new tab). Despite critical reviews, the team said their experiment represents the first time a living animal was quantum entangled.

And in March 2022, NASA announced (opens in new tab) it would be sending a quantum entanglement experiment to space. The experiment, called the Space Entanglement and Annealing Quantum Experiment, or SEAQUE, will test two quantum computers in the harsh environment of space.

For a more in-depth definition and exploration of quantum entanglement, check out Jed Brody's "Quantum Entanglement (The MIT Press Essential Knowledge series) (opens in new tab)" (Knopf, 2008). Read the fascinating stories about what life was like at the time of quantum entanglement's discovery in Louisa Gilder's "The Age of Entanglement: When Quantum Physics Was Reborn (opens in new tab)" (Deckle Edge, 2008). Or, take a broader look at quantum physics as a whole in this book, "Quantum Physics for Beginners: From Wave Theory to Quantum Computing. Understanding How Everything Works by a Simplified Explanation of Quantum Physics and Mechanics Principles (opens in new tab)" by Carl J. Pratt (Independently published, 2021).

Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.[1]

Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior gives rise to seemingly paradoxical effects: any measurement of a particle's properties results in an irreversible wave function collapse of that particle and changes the original quantum state. With entangled particles, such measurements affect the entangled system as a whole.

Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen,[2] and several papers by Erwin Schrödinger shortly thereafter,[3][4] describing what came to be known as the EPR paradox. Einstein and others considered such behavior impossible, as it violated the local realism view of causality (Einstein referring to it as "spooky action at a distance")[5] and argued that the accepted formulation of quantum mechanics must therefore be incomplete.

According to some interpretations of quantum mechanics, the effect of one measurement occurs instantly. Other interpretations which do not recognize wavefunction collapse dispute that there is any "effect" at all. However, all interpretations agree that entanglement produces correlation between the measurements, and that the mutual information between the entangled particles can be exploited, but that any transmission of information at faster-than-light speeds is impossible.[9][10]

Quantum entanglement has been demonstrated experimentally with photons,[11][12] neutrinos,[13] electrons,[14][15] molecules as large as buckyballs,[16][17] and even small diamonds.[18] The utilization of entanglement in communication, computation and quantum radar is a very active area of research and development.

Schrödinger shortly thereafter published a seminal paper defining and discussing the notion of "entanglement." In the paper, he recognized the importance of the concept, and stated:[3] "I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity.[21] Einstein later famously derided entanglement as "spukhafte Fernwirkung"[22] or "spooky action at a distance."

The EPR paper generated significant interest among physicists, which inspired much discussion about the foundations of quantum mechanics and Bohm's interpretation in particular, but produced relatively little other published work. Despite the interest, the weak point in EPR's argument was not discovered until 1964, when John Stewart Bell proved that one of their key assumptions, the principle of locality, as applied to the kind of hidden variables interpretation hoped for by EPR, was mathematically inconsistent with the predictions of quantum theory.

Bell's work raised the possibility of using these super-strong correlations as a resource for communication. It led to the 1984 discovery of quantum key distribution protocols, most famously BB84 by Charles H. Bennett and Gilles Brassard[29] and E91 by Artur Ekert.[30] Although BB84 does not use entanglement, Ekert's protocol uses the violation of a Bell's inequality as a proof of security.

In 2022, the Nobel Prize in Physics was awarded to Aspect, Clauser, and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".[31]

An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole. In entanglement, one constituent cannot be fully described without considering the other(s). 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 cannot be written as a single product term.

Quantum systems can become entangled through various types of interactions. For some ways in which entanglement may be achieved for experimental purposes, see the section below on methods. Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made.[32]

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-1/2 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.)

The above result may or may not be perceived as surprising. A classical system would display the same property, and a hidden variable theory would certainly be required to do so, based on conservation of angular momentum in classical and quantum mechanics alike. The difference is that a classical system has definite values for all the observables all along, while the quantum system does not. In a sense to be discussed below, the quantum system considered here seems to acquire a probability distribution for the outcome of a measurement of the spin along any axis of the other particle upon measurement of the first particle. This probability distribution is in general different from what it would be without measurement of the first particle. This may certainly be perceived as surprising in the case of spatially separated entangled particles.

(In fact similar paradoxes can arise even without entanglement: the position of a single particle is spread out over space, and two widely separated detectors attempting to detect the particle in two different places must instantaneously attain appropriate correlation, so that they do not both detect the particle.)

A possible resolution to the paradox is to assume that quantum theory is incomplete, and the result of measurements depends on predetermined "hidden variables".[34] The state of the particles being measured contains some hidden variables, whose values effectively determine, right from the moment of separation, what the outcomes of the spin measurements are going to be. This would mean that each particle carries all the required information with it, and nothing needs to be transmitted from one particle to the other at the time of measurement. Einstein and others (see the previous section) originally believed this was the only way out of the paradox, and the accepted quantum mechanical description (with a random measurement outcome) must be incomplete.