Continuity of the robustness of contextuality of empirical models

• DOI: 10.1007/s11433-016-0210-2
• Publication Date: 2016-07-29T19:59:46Z
• Authors: HuiXian Meng; HuaiXin Cao; WenHua Wang; Liang Chen; Yajing Fan
• Keywords: Kochen–Specker theorem; Robustness; Astron

Recently, the robustness of contextuality (RoC) of an empirical model was discussed in [Sci. China-Phys. Mech. Astron. 59, 640303 (2016)], many important properties of the RoC have been proved except for its boundedness and continuity. The aim of this paper is to find an upper bound for the RoC over all of empirical models and prove that the RoC is a continuous function on the set of all empirical models. Lastly, a relationship between the RoC and the extent of violating the noncontextual inequalities is established for an n-cycle contextual box. This relationship implies that the RoC can be used to quantify the contextuality of n-cycle boxes.