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Logical Bell Inequalities | | Samson Abramsky
; Lucien Hardy
; | | Date: |
7 Mar 2012 | | Abstract: | We develop a logical method for deriving Bell inequalities. This approach is
both conceptually illuminating and technically powerful. We show that a
rational inequality is satisfied by all non-contextual models if and only if it
is equivalent to a logical Bell inequality. Thus quantitative tests for
contextuality or non-locality always hinge on purely logical consistency
conditions. We obtain explicit descriptions of complete sets of inequalities
for the convex polytope of non-contextual probability models, and the derived
polytope of expectation values for these models. Moreover, these results are
obtained for general measurement covers, following the sheaf-theoretic approach
to non-locality and contextuality introduced by the first author and Adam
Brandenburger. Thus they apply to a wide range of situations, including $(n, k,
2^p)$ Bell scenarios, and all Kochen-Specker configurations. We also obtain
results for a number of special cases. We show that a model achieves maximal
violation of a logical Bell inequality if and only if it is strongly
contextual. We show that all Kochen-Specker configurations lead to maximal
violations of logical Bell inequalities in a state-independent fashion. We also
derive specific violations of logical Bell inequalities for models which are
possibilistically contextual, meaning that they admit logical proofs of
contextuality. | | Source: | arXiv, 1203.1352 | | Services: | Forum | Review | PDF | Favorites | |
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