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 ...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） ＆gt; 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） ＆gt; 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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.1137101211401359+1 种基金11471200 and 11571213)the Fundamental Research Funds for the Central Universities(Grant No.GK201301007)
文摘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） ＆gt; 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） ＆gt; 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.
