The robustness of contextuality and the contextuality cost of empirical models

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• 作者：HuiXian Meng ; HuaiXin Cao ; WenHua Wang
• 关键词：relative robustness ; robustness of contextuality ; contextuality cost ; empirical model
• 刊名：SCIENCE CHINA Physics, Mechanics & Astronomy
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：59
• 期：4
• 全文大小：629 KB
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• 作者单位：HuiXian Meng (1)
  HuaiXin Cao (1)
  WenHua Wang (2)
  
  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China
  2. School of Ethnic Nationalities Education, Shaanxi Normal University, Xi’an, 710062, China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Chinese Library of Science
  Mechanics, Fluids and Thermodynamics
  Physics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1927

文摘

In this paper, we introduce and discuss the robustness of contextuality (RoC) 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 RoC function R _C is convex, lower semi-continuous and un-increasing under an affine mapping on the set EM 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 R _C (e) and C(e) 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 0.5 is found for the RoC of all no-signaling type (2, 2, 2) empirical models.