Generalized Robustness of Contextuality

Abstract

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 ∆ e of violating the non-contextual inequalities is established.

One-Shot Manipulation of Dynamical Quantum Resources

“…This is incorporated in our framework by considering the set of all classical-classical channels for consistent boxes [67] as O all and the set of channels corresponding to noncontextual boxes as O. Our results characterize the exact and approximate box transformations with operations that do not create contextuality, offering a new perspective to the recent resource-theoretic framework [44,45,103], as well as providing operational application of the robustness of contextuality [104][105][106], contextual fraction [67,68,107], and hypothesis testing measures introduced in this work.…”

Certification and applications of quantum nonlocal correlations

“…A related quantification of steering, the generalized steering robustness, is proposed in [250], in a similar way as what is done for the generalized entanglement robustness [251,252]. This quantification is proven to have desirable characteristics for a proper steering measure.…”