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 ...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11371012,11401359,11471200,11571211 and11571213)the Fundamental Research Funds for the Central Universities(Grant No.GK201604001)the Innovation Fund Project for Graduate Program of Shaanxi Normal University(Grant No.2016CBY005)
文摘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.
