The robustness of contextuality and the contextual

Authors: HuiXian Meng HuaiXin Cao WenHua Wang

Publish Date: 2016/02/26

Volume: 59, Issue: 4, Pages: 640303-

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Abstract

In this paper we introduce and discuss the robustness of contextuality RoC R C e and the contextuality cost Ce of an empirical model e The following properties of them are proved i An empirical model e is contextual if and only if R C e 0 ii the RoC function R C is convex lower semicontinuous and unincreasing under an affine mapping on the set EM of all empirical models iii e is noncontextual if and only if Ce = 0 iv e is contextual if and only if Ce 0 v e is strongly contextual if and only if Ce = 1 Also a relationship between R C e and Ce is obtained Lastly the RoC of three empirical models is computed and compared Especially the RoC of the PR boxes is obtained and the supremum 05 is found for the RoC of all nosignaling type 2 2 2 empirical models

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