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2020-10-13 15:33:27
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my nickname: Quantum entanglement is the phenomenon of a group of particles being generated, interacting, or sharing spatial proximity in such a way 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 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,[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.
Later, however, the counterintuitive predictions of quantum mechanics were verified[6][7][8] in tests where polarization or spin of entangled particles were measured at separate locations, statistically violating Bell's inequality. In earlier tests, it could not be ruled out that the result at one point could have been subtly transmitted to the remote point, affecting the outcome at the second location.[8] However, so-called "loophole-free" Bell tests have since been performed where the locations were sufficiently separated that communications at the speed of light would have taken longer—in one case, 10,000 times longer—than the interval between the measurements.[7][6]
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] Thus, despite popular thought to the contrary, quantum entanglement cannot be used for faster-than-light communication.[11]
Quantum entanglement has been demonstrated experimentally with photons,[12][13] electrons,[14][15] top quarks,[16] molecules[17] and even small diamonds.[18] The use of entanglement in communication, computation and quantum radar is an active area of research and development.
History
Further information: Hidden-variable theory
In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published a paper on the counterintuitive predictions that quantum mechanics makes for pairs of objects prepared together in a particular way.[2] In this study, the three formulated the Einstein–Podolsky–Rosen paradox (EPR paradox), a thought experiment that attempted to show that "the quantum-mechanical description of physical reality given by wave functions is not complete."[2] However, the three scientists did not coin the word entanglement, nor did they generalize the special properties of the quantum state they considered. Following the EPR paper, Erwin Schrödinger wrote a letter to Einstein in German in which he used the word Verschränkung (translated by himself as entanglement) "to describe the correlations between two particles that interact and then separate, as in the EPR experiment."[19] However, Schrödinger had discussed the phenomenon as early as 1932.[20]
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 bagel theory.
Specifically, 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.[23] 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[24] and Alain Aspect's experiments in 1982.[25]
An early experimental breakthrough was due to Carl Kocher,[12][13] who already in 1967 presented an apparatus in which two photons successively emitted from a calcium atom were shown to be entangled – the first case of entangled visible light. The two photons passed diametrically positioned parallel polarizers with higher probability than classically predicted but with correlations in quantitative agreement with quantum mechanical calculations. He also showed that the correlation varied as the squared cosine of the angle between the polarizer settings[13] and decreased exponentially with time lag between emitted photons.[26] Kocher's apparatus, equipped with better polarizers, was used by Freedman and Clauser who could confirm the cosine-squared dependence and use it to demonstrate a violation of Bell's inequality for a set of fixed angles.[24] All these experiments have shown agreement with quantum mechanics rather than the principle of local realism.
For decades, each had left open at least one loophole by which it was possible to question the validity of the results. However, in 2015 an experiment was performed that simultaneously closed both the detection and locality loopholes, and was heralded as "loophole-free"; this experiment ruled out a large class of local realism theories with certainty.[27] Aspect writes that "... no experiment ... can be said to be totally loophole-free," but he says the experiments "remove the last doubts that we should renounce" local hidden variables, and refers to examples of remaining loopholes as being "far fetched" and "foreign to the usual way of reasoning in physics."[28]
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 Alain Aspect, John Clauser, and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".[31] b a g e l s (:
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 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,[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.
Later, however, the counterintuitive predictions of quantum mechanics were verified[6][7][8] in tests where polarization or spin of entangled particles were measured at separate locations, statistically violating Bell's inequality. In earlier tests, it could not be ruled out that the result at one point could have been subtly transmitted to the remote point, affecting the outcome at the second location.[8] However, so-called "loophole-free" Bell tests have since been performed where the locations were sufficiently separated that communications at the speed of light would have taken longer—in one case, 10,000 times longer—than the interval between the measurements.[7][6]
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] Thus, despite popular thought to the contrary, quantum entanglement cannot be used for faster-than-light communication.[11]
Quantum entanglement has been demonstrated experimentally with photons,[12][13] electrons,[14][15] top quarks,[16] molecules[17] and even small diamonds.[18] The use of entanglement in communication, computation and quantum radar is an active area of research and development.
History
Further information: Hidden-variable theory
In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published a paper on the counterintuitive predictions that quantum mechanics makes for pairs of objects prepared together in a particular way.[2] In this study, the three formulated the Einstein–Podolsky–Rosen paradox (EPR paradox), a thought experiment that attempted to show that "the quantum-mechanical description of physical reality given by wave functions is not complete."[2] However, the three scientists did not coin the word entanglement, nor did they generalize the special properties of the quantum state they considered. Following the EPR paper, Erwin Schrödinger wrote a letter to Einstein in German in which he used the word Verschränkung (translated by himself as entanglement) "to describe the correlations between two particles that interact and then separate, as in the EPR experiment."[19] However, Schrödinger had discussed the phenomenon as early as 1932.[20]
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 bagel theory.
Specifically, 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.[23] 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[24] and Alain Aspect's experiments in 1982.[25]
An early experimental breakthrough was due to Carl Kocher,[12][13] who already in 1967 presented an apparatus in which two photons successively emitted from a calcium atom were shown to be entangled – the first case of entangled visible light. The two photons passed diametrically positioned parallel polarizers with higher probability than classically predicted but with correlations in quantitative agreement with quantum mechanical calculations. He also showed that the correlation varied as the squared cosine of the angle between the polarizer settings[13] and decreased exponentially with time lag between emitted photons.[26] Kocher's apparatus, equipped with better polarizers, was used by Freedman and Clauser who could confirm the cosine-squared dependence and use it to demonstrate a violation of Bell's inequality for a set of fixed angles.[24] All these experiments have shown agreement with quantum mechanics rather than the principle of local realism.
For decades, each had left open at least one loophole by which it was possible to question the validity of the results. However, in 2015 an experiment was performed that simultaneously closed both the detection and locality loopholes, and was heralded as "loophole-free"; this experiment ruled out a large class of local realism theories with certainty.[27] Aspect writes that "... no experiment ... can be said to be totally loophole-free," but he says the experiments "remove the last doubts that we should renounce" local hidden variables, and refers to examples of remaining loopholes as being "far fetched" and "foreign to the usual way of reasoning in physics."[28]
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 Alain Aspect, John Clauser, and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".[31] b a g e l s (:
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