Quantum entanglement
[1]: 867 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.Later, however, 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.[6][7][8][9] 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.However, despite the fact that entanglement can produce statistical correlations between events in widely separated places, it cannot be used for faster-than-light communication.Albert Einstein and Niels Bohr engaged in a long-running collegial dispute about the meaning of quantum mechanics, now known as the Bohr–Einstein debates.[23] In 1935, Grete Hermann studied the mathematics of an electron interacting with a photon and noted the phenomenon that would come to be called entanglement.[24] Later that same year, Einstein, Boris Podolsky and Nathan Rosen published a paper on what is now known as the Einstein–Podolsky–Rosen (EPR) paradox, a thought experiment that attempted to show that "the quantum-mechanical description of physical reality given by wave functions is not complete".Shortly after this paper appeared, Erwin Schrödinger wrote a letter to Einstein in German in which he used the word Verschränkung (translated by himself as entanglement) to describe situations like that of the EPR scenario."[3] 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.[30] Chien-Shiung Wu and I. Shaknov carried out this experiment in 1949,[31] thereby demonstrating that the entangled particle pairs considered by EPR could be created in the laboratory.[44][45] 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"."[54] 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.[60] A possible resolution to the paradox is to assume that quantum theory is incomplete, and the result of measurements depends on predetermined "hidden variables".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.It has been proven mathematically that compatible measurements cannot show Bell-inequality-violating correlations,[66] and thus entanglement is a fundamentally non-classical phenomenon.[70] It is sometimes argued that using the term nonlocality carries the unwarranted implication that the violation of Bell inequalities must be explained by physical, faster-than-light signals.[75] Moreover, quantum field theory is often said to be local because observables defined within spacetime regions that are spacelike separated must commute.[51]: 131 In quantum information theory, entangled states are considered a 'resource', i.e., something costly to produce and that allows implementing valuable transformations.[120] A density matrix ρ is called separable if it can be written as a convex sum of product states, namelyA numerical approach to the problem is suggested by Jon Magne Leinaas, Jan Myrheim and Eirik Ovrum in their paper "Geometrical aspects of entanglement".Specifically, Simon[130] formulated a particular version of the Peres–Horodecki criterion in terms of the second-order moments of canonical operators and showed that it is necessary and sufficient forSimon's condition can be generalized by taking into account the higher order moments of canonical operators[133][134] or by using entropic measures.Part of the effort to reconcile these approaches to time results in the Wheeler–DeWitt equation, which predicts the state of the universe is timeless or static, contrary to ordinary experience.To date, all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave.[9] 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.[8][7][15][36] In 2017, Yin et al. reported setting a new quantum entanglement distance record of 1,203 km, demonstrating the survival of a two-photon pair and a violation of a Bell inequality, reaching a CHSH valuation of 2.37±0.09, under strict Einstein locality conditions, from the Micius satellite to bases in Lijian, Yunnan and Delingha, Quinhai, increasing the efficiency of transmission over prior fiberoptic experiments by an order of magnitude.[150] The experiment was carried by the ATLAS detector measuring the spin of top-quark pair production and the effect was observed with a more than 5σ level of significance, the top quark is the heaviest known particle and therefore has a very short lifetime ([151] The spin polarization and correlation of the particles was measured and tested for entanglement with concurrence as well as the Peres–Horodecki criterion and subsequently the effect has been confirmed too in the CMS detector.[152][153] In 2020, researchers reported the quantum entanglement between the motion of a millimetre-sized mechanical oscillator and a disparate distant spin system of a cloud of atoms.[160] Physicists at Brookhaven National Laboratory demonstrated quantum entanglement within protons, showing quarks and gluons are interdependent rather than isolated particles.
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