Reformulating noncontextuality inequalities in an operational approach

Abstract

A new theory-independent noncontextuality inequality is presented [Phys. Rev. Lett. 115, 110403 (2015)] based on Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing novel noncontextuality inequalities, we show that such result can be generalized from KS set to the noncontextuality inequalities not only for state-independent but also for state-dependent scenario. The YO-13 ray and $n$ cycle ray are considered as examples.

6 pages, 3 figures. Published version

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• From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities
• Characterising and bounding the set of quantum behaviours in contextuality scenarios
• Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
• Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states
• Quantitative relations between different measurement contexts
• Revealing quantum contextuality using a single measurement device
• Tracing quantum correlations back to collective interferences
• Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
• Twenty years of quantum contextuality at USTC
• Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations