General conditions for maximal violation of non-contextuality in discrete and continuous variables

Abstract

The contextuality of quantum mechanics, i.e. the measurement outcome dependence upon previously made measurements, can be shown by the violation of inequalities based on measurements of well chosen observables. An important property of such observables is that their expectation value can be expressed in terms of probabilities of obtaining two exclusive outcomes. In order to satisfy this, inequalities have been constructed using either observables with a dichotomic spectrum or using periodic functions obtained from displacement operators in phase space. Here we identify the general conditions on the spectral decomposition of observables demonstrating state independent contextuality of quantum mechanics. As a consequence, our results not only unify existing strategies for maximal violation of state independent non-contextual inequalities but also lead to new scenarii enabling such violation. Among the consequences of our results is the impossibility of having a state independent maximal violation of non-contextuality in the Peres-Mermin scenario with discrete observables of odd dimensions.

6 pages

References in corpus (9)

• Experimentally testable state-independent quantum contextuality
• State-independent experimental test of quantum contextuality
• State-independent quantum contextuality with single photons
• Universality of state-independent violation of correlation inequalities for noncontextual theories
• Experimental implementation of a Kochen-Specker set of quantum tests
• Quantum information processing in phase space: A modular variables approach
• State-independent quantum contextuality for continuous variables
• Contextuality in phase space
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Cited by in corpus (8)

• Kochen-Specker Contextuality
• Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
• Uncertainty Relations for coarse-grained measurements: an overview
• No-broadcasting characterizes operational contextuality
• Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
• Continuous-variable nonlocality and contextuality
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• Periodic discretized continuous observables are neither continuous nor discrete