Abstract
One Investigates inequalities for the probabilities and mathematical expectations which follow from the postulates of the local quantum theory. It turns out that the relation between the quantum and the classical correlation matrices is expressed] in terms of Grothendieck's known constant. It is also shown that the extremal quantum correlations characterize the Clifford algebra (i.e., canonical anticommutative relations).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 174–194, 1985.
The author is grateful to A. M. Vershik for formulating the problem of the quantum analogues of Bell's inequalities and to L. A. Khalfin for formulating the problem of the representations of extrernal quantum correlations.
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Tsirel'son, B.S. Quantum analogues of the Bell inequalities. The case of two spatially separated domains. J Math Sci 36, 557–570 (1987). https://doi.org/10.1007/BF01663472
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DOI: https://doi.org/10.1007/BF01663472