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In this paper, we introduce and discuss the robustness of contextuality(Ro C) R_C(e) and the contextuality cost C(e) 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 Ro C function R_C is convex, lower semi-continuous and un-increasing under an affine mapping on the set E M of all empirical models;(iii) e is non-contextual if and only if C(e) = 0;(iv) e is contextual if and only if C(e) > 0;(v) e is strongly contextual if and only if C(e) = 1. Also, a relationship between RC(e) and C(e) is obtained. Lastly, the Ro C of three empirical models is computed and compared. Especially, the Ro C of the PR boxes is obtained and the supremum 0.5 is found for the Ro C of all no-signaling type(2, 2, 2) empirical models.
In this paper, we introduce and discuss the robustness of contextuality (Ro C) R_C (e) and the contextuality cost C (e) 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 Ro C function R_C is convex, lower semi-continuous and un-increasing under an affine mapping on the set EM of all empirical models; -contextual if and only if C (e) = 0; (iv) e is contextual if and only if C (e)> 0; (v) e is strongly contextual if and only if C Lastly, the Ro C of three empirical models are computed and compared. Especially, the Ro C of the PR boxes is obtained and the supremum 0.5 is found for the Ro C of all no-signaling type (2, 2, 2) insight models.