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Entropy 2016, 18(9), 297; doi:10.3390/e18090297

Generalized Robustness of Contextuality

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
*
Author to whom correspondence should be addressed.
Academic Editor: Jay Lawrence
Received: 16 May 2016 / Revised: 4 August 2016 / Accepted: 9 August 2016 / Published: 1 September 2016
(This article belongs to the Special Issue Quantum Information 2016)
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Abstract

Motivated by the importance of contextuality and a work on the robustness of the entanglement of mixed quantum states, the robustness of contextuality (RoC) R C ( e ) of an empirical model e against non-contextual noises was introduced and discussed in Science China Physics, Mechanics and Astronomy (59(4) and 59(9), 2016). Because noises are not always non-contextual, this paper introduces and discusses the generalized robustness of contextuality (GRoC) R g ( e ) of an empirical model e against general noises. It is proven that R g ( e ) = 0 if and only if e is non-contextual. This means that the quantity R g can be used to distinguish contextual empirical models from non-contextual ones. It is also shown that the function R g is convex on the set of all empirical models and continuous on the set of all no-signaling empirical models. For any two empirical models e and f such that the generalized relative robustness of e with respect to f is finite, a fascinating relationship between the GRoCs of e and f is proven, which reads R g ( e ) R g ( f ) 1 . Lastly, for any n-cycle contextual box e, a relationship between the GRoC R g ( e ) and the extent Δ e of violating the non-contextual inequalities is established. View Full-Text
Keywords: empirical models; contextuality; non-contextuality; generalized relative robustness of contextuality; generalized robustness of contextuality; non-contextual inequalities empirical models; contextuality; non-contextuality; generalized relative robustness of contextuality; generalized robustness of contextuality; non-contextual inequalities
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Meng, H.; Cao, H.; Wang, W.; Fan, Y.; Chen, L. Generalized Robustness of Contextuality. Entropy 2016, 18, 297.

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