Generalized Robustness of Contextuality
School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
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
Motivated by the importance of contextuality and a work on the robustness of the entanglement of mixed quantum states, the robustness of contextuality (RoC)
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)
of an empirical model e
against general noises. It is proven that
if and only if e
is non-contextual. This means that the quantity
can be used to distinguish contextual empirical models from non-contextual ones. It is also shown that the function
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
such that the generalized relative robustness of e
with respect to f
is finite, a fascinating relationship between the GRoCs of e
is proven, which reads
. Lastly, for any n
-cycle contextual box e
, a relationship between the GRoC
and the extent
of violating the non-contextual inequalities is established.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Meng, H.; Cao, H.; Wang, W.; Fan, Y.; Chen, L. Generalized Robustness of Contextuality. Entropy 2016, 18, 297.
Meng H, Cao H, Wang W, Fan Y, Chen L. Generalized Robustness of Contextuality. Entropy. 2016; 18(9):297.
Meng, Huixian; Cao, Huaixin; Wang, Wenhua; Fan, Yajing; Chen, Liang. 2016. "Generalized Robustness of Contextuality." Entropy 18, no. 9: 297.
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