Samson Abramsky, Lucien Hardy
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.
View original:
http://arxiv.org/abs/1203.1352
No comments:
Post a Comment