Mermin's n-particle Bell inequality and operators' noncommutativity
Abstract
The relationship between the noncommutativity of operators and the violation of the Bell inequality is exhibited in the light of the n-particle Bell-type inequality discovered by Mermin [PRL 65, 1838 (1990)]. It is shown, in particular, that the maximal amount of violation of Mermin's inequality predicted by quantum mechanics decreases exponentially by a factor of 2-m/2 whenever any m among the n single-particle commutators happen to vanish.
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