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EPR-Bohm experiment and Bell’s inequality: Quantum physics meets probability theory. (English. Russian original) Zbl 1155.81313
Theor. Math. Phys. 157, No. 1, 1448-1460 (2008); translation from Teor. Mat. Fiz. 157, No. 1, 99-115 (2008).
Summary: Our main aim in this paper is to inform the physics community (and especially experts in quantum information) about investigations of the problem of the probabilistic compatibility of a family of random variables: the possibility of realizing such a family based on a single probability measure (of constructing a single Kolmogorov probability space). These investigations were started a hundred years ago by Boole. The complete solution of the problem was obtained by the Soviet mathematician Vorobiev in the 1960s. It turns out that probabilists and statisticians obtained inequalities for probabilities and correlations that include the famous Bell’s inequality and its generalizations.

MSC:
81P15 Quantum measurement theory, state operations, state preparations
81P68 Quantum computation
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