Quantum entanglement
Quantum entanglement is the phenomenon wherein the quantum state of each particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.
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. This behavior gives rise to seemingly paradoxical effects: any measurement of a particle's properties results in an apparent and 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, and several papers by Erwin Schrödinger shortly thereafter, 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 and argued that the accepted formulation of quantum mechanics must therefore be incomplete.
Later, the counterintuitive predictions of quantum mechanics were verified in tests where polarization or spin of entangled particles were measured at separate locations, statistically violating Bell's inequality. This established that the correlations produced from quantum entanglement cannot be explained in terms of local hidden variables, i.e., properties contained within the individual particles themselves.
Entanglement can produce statistical correlations between events in widely separated places, but it cannot be used for faster-than-light communication.
Quantum entanglement has been demonstrated experimentally with photons, electrons, top quarks, molecules and even small diamonds. The use of quantum entanglement in communication and computation is an active area of research and development.
History
Albert Einstein and Niels Bohr engaged in a long-running collegial dispute over the interpretation of quantum mechanics, now known as the Bohr–Einstein debates. During these debates, Einstein introduced a thought experiment involving a box that emits a photon. He noted that the experimenter's choice of which measurement to make on the box would change what can be predicted about the photon, even when the photon is very far away. This argument, which Einstein had formulated by 1931, was an early recognition of what would later be called entanglement. That same year, Hermann Weyl observed in his textbook on group theory and quantum mechanics that quantum systems composed of multiple interacting parts exhibit a kind of Gestalt, in which "the whole is greater than the sum of its parts". In 1932, Erwin Schrödinger derived the defining equations of quantum entanglement but left them unpublished. In 1935, Grete Hermann studied the mathematics of an electron interacting with a photon and noted the phenomenon that would later be called entanglement. Later that same year, Einstein, Boris Podolsky and Nathan Rosen published a paper on what is now known as the Einstein–Podolsky–Rosen paradox, a thought experiment that attempted to show that "the quantum-mechanical description of physical reality given by wave functions is not complete". Their thought experiment considered two systems that interact and then separate, and they argued that, afterward, quantum mechanics could not describe the two systems individually.Shortly after this paper appeared, Erwin Schrödinger wrote a letter to Einstein in German in which he used the word Verschränkung to describe situations like that of the EPR scenario. Schrödinger followed up with a full paper defining and discussing the notion of entanglement, saying "I would not call 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. Einstein later disparaged quantum mechanics for seemingly exhibiting "spukhafte Fernwirkung" or "spooky action at a distance", meaning the acquisition of a value of a property at one location resulting from a measurement at a distant location.
In 1946, John Archibald Wheeler suggested studying the polarization of pairs of gamma-ray photons produced by electron–positron annihilation. Chien-Shiung Wu and I. Shaknov carried out this experiment in 1949, thereby demonstrating that the entangled particle pairs considered by EPR could be created in the laboratory.
Despite Schrödinger's claim of its importance, little work on entanglement was published for decades after his paper was published. In 1964 John S. Bell demonstrated an upper limit, seen in Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and showed that quantum theory predicts violations of this limit for certain entangled systems. His inequality is experimentally testable, and there have been numerous relevant experiments, starting with the pioneering work of Stuart Freedman and John Clauser in 1972 and Alain Aspect's experiments in 1982.
While Bell actively discouraged students from pursuing work like his as too esoteric, after a talk at Oxford a student named Artur Ekert suggested that the violation of a Bell inequality could be used as a resource for communication. Ekert followed up by publishing a quantum key distribution protocol called E91 based on it.
In 1992, the entanglement concept was leveraged to propose quantum teleportation, an effect that was realized experimentally in 1997.
Beginning in the mid-1990s, Anton Zeilinger used the generation of entanglement via parametric down-conversion to develop entanglement swapping and demonstrate quantum cryptography with entangled photons.
In 2022, the Nobel Prize in Physics was awarded to Aspect, Clauser, and Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".
Concept
Meaning of entanglement
Just as energy is a resource that facilitates mechanical operations, entanglement is a resource that facilitates performing tasks that involve communication and computation. The mathematical definition of entanglement can be paraphrased as saying that maximal knowledge about the whole of a system does not imply maximal knowledge about the individual parts of that system. If the quantum state that describes a pair of particles is entangled, then the results of measurements upon one half of the pair can be strongly correlated with the results of measurements upon the other. However, entanglement is not the same as "correlation" as understood in classical probability theory and in daily life. Instead, entanglement can be thought of as potential correlation that can be used to generate actual correlation in an appropriate experiment. The correlations generated from an entangled quantum state cannot in general be replicated by classical probability.An example of entanglement is a subatomic particle that 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. For instance, a spin-zero particle could decay into a pair of spin-1/2 particles. If there is no orbital angular momentum, the total spin angular momentum after this decay must be zero. 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 the pair is said to be in the singlet state. Perfect anti-correlations like this could be explained by "hidden variables" within the particles. For example, we could hypothesize that the particles are made in pairs such that one carries a value of "up" while the other carries a value of "down". Then, knowing the result of the spin measurement upon one particle, we could predict that the other will have the opposite value. Bell illustrated this with a story about a colleague, Bertlmann, who always wore socks with mismatching colors. "Which colour he will have on a given foot on a given day is quite unpredictable," Bell wrote, but upon observing "that the first sock is pink you can be already sure that the second sock will not be pink." Revealing the remarkable features of quantum entanglement requires considering multiple distinct experiments, such as spin measurements along different axes, and comparing the correlations obtained in these different configurations.
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. In more detail, this process involves the particles becoming entangled with the environment, as a consequence of which, the quantum state describing the particles themselves is no longer entangled.
Mathematically, an entangled system can be 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. When entanglement is present, one constituent cannot be fully described without considering the other. 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.