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arXiv · 1410.4935

Mathematical and physical meaning of the Bell inequalities

Emilio Santos
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Abstract

It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, thus showing a conflict between quantum mechanics and local realism (Bell's theorem). The relations of the Bell inequalities with contextuality, Kochen-Specker theorem, and quantum entanglement are briefly discussed.

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Emilio Santos. 2016-03-26. Mathematical and physical meaning of the Bell inequalities. https://doi.org/10.1088/0143-0807%2F37%2F5%2F055402

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