Robust preparation noncontextuality inequalities in the simplest scenario

Abstract

Contextuality is the leading notion of nonclassicality for a single system. However, an experimental demonstration requires finding procedures that are operationally equivalent, which might seem impossible to achieve exactly. Here I focus on the simplest non-trivial case, four preparations and two tomographically complete binary measurements. Exploiting a subtle connection to the CHSH scenario gives eight non-linear inequalities which are together necessary and sufficient for the experimental statistics to admit a preparation noncontextual model in such a scenario. No fixed operational equivalences are required, removing a key difficulty with experimental tests of older preparation noncontextuality inequalities.

5+3 pages, 2 figures, and a small Mathematica notebook. v3: Minor fixes and removal of allegedly non-informative word from title

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Cited by in corpus (29)

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• Why interference phenomena do not capture the essence of quantum theory
• Sharing non-locality and non-trivial preparation contextuality using same family of Bell expressions
• Preparation contextuality as an essential feature underlying quantum communication advantage
• Aspects of the phenomenology of interference that are genuinely nonclassical
• What is nonclassical about uncertainty relations?
• Characterising and bounding the set of quantum behaviours in contextuality scenarios
• Contextuality in entanglement-assisted one-shot classical communication
• Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness
• An invertible map between Bell non-local and contextuality scenarios
• Quantum prescriptions are more ontologically distinct than they are operationally distinguishable
• A linear program for testing nonclassicality and an open-source implementation
• Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
• Testing quantum theory by generalizing noncontextuality
• Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios
• Contextuality in anomalous heat flow
• Alternative robust ways of witnessing nonclassicality in the simplest scenario
• Geometry of joint reality: device-independent steering and operational completeness
• Contextuality witness inspired by optimal state discrimination
• Connecting XOR and XOR* games
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Two definitions of maximally $\psi$-epistemic ontological model and preparation non-contextuality
• Experimentally ruling out joint reality based on operational completeness
• Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
• Demonstration of universal contextuality through communication games free of both operational inequivalence and compatibility loopholes
• Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations
• Typicality of Contextuality