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In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics cannot be reproduced by local hidden variable theories. Experimental verification of violation of the inequalities is seen as experimental confirmation that nature cannot be described by local hidden variables theories. CHSH stands for John Clauser, Michael Horne, Abner Shimony, and Richard Holt, who described it in a much-cited paper published in 1969 (Clauser ''et al.'', 1969).〔 They derived the CHSH inequality, which, as with John Bell's original inequality (Bell, 1964),〔, reproduced as Ch. 2 of 〕 is a constraint on the statistics of "coincidences" in a Bell test experiment which is necessarily true if there exist underlying local hidden variables (local realism). This constraint can, on the other hand, be infringed by quantum mechanics. == Statement of the inequality == The usual form of the CHSH inequality is: :where ''a'' and ''a''′ are detector settings on side A, ''b'' and ''b''′ on side B, the four combinations being tested in separate subexperiments. The terms ''E''(''a'', ''b'') etc. are the quantum correlations of the particle pairs, where the quantum correlation is defined to be the expectation value of the product of the "outcomes" of the experiment, i.e. the statistical average of ''A''(''a'')·''B''(''b''), where ''A'' and ''B'' are the separate outcomes, using the coding +1 for the '+' channel and −1 for the '−' channel. Clauser et al.'s 1969 derivation was oriented towards the use of "two-channel" detectors, and indeed it is for these that it is generally used, but under their method the only possible outcomes were +1 and −1. In order to adapt it to real situations, which at the time meant the use of polarised light and single-channel polarisers, they had to interpret '−' as meaning "non-detection in the '+' channel", i.e. either '−' or nothing. They did not in the original article discuss how the two-channel inequality could be applied in real experiments with real imperfect detectors, though it was later proved (Bell, 1971)〔J. S. Bell, in ''Foundations of Quantum Mechanics'', Proceedings of the International School of Physics “Enrico Fermi”, Course XLIX, B. d’Espagnat (Ed.) (Academic, New York, 1971), p. 171 and Appendix B. Pages 171-81 are reproduced as Ch. 4 of J. S. Bell, ''Speakable and Unspeakable in Quantum Mechanics'' (Cambridge University Press 1987)〕 that the inequality itself was equally valid. The occurrence of zero outcomes, though, means it is no longer so obvious how the values of ''E'' are to be estimated from the experimental data. The mathematical formalism of quantum mechanics predicts a maximum value for S of 2, which is greater than 2, and CHSH violations are therefore predicted by the theory of quantum mechanics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「CHSH inequality」の詳細全文を読む スポンサード リンク
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