A linear program for testing nonclassicality and an open-source implementation

Abstract

A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an open-source implementation of it which tests whether or not any given prepare-measure experiment is classically-explainable in this sense. The input to the program is simply an arbitrary set of quantum states and an arbitrary set of quantum effects; the program then determines if the Born rule statistics generated by all pairs of these can be explained by a classical (noncontextual) model. If a classical model exists, it provides an explicit model. If it does not, then it computes the minimal amount of noise that must be added such that a model does exist, and then provides this model. We generalize all these results to arbitrary generalized probabilistic theories (and accessible fragments thereof) as well; indeed, our linear program is a test of simplex-embeddability.

4 pages plus appendices, 4 figures and many diagrams. Comments welcome!

References in corpus (9)

• Negativity and contextuality are equivalent notions of nonclassicality
• Anomalous Weak Values Are Proofs of Contextuality
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• Why interference phenomena do not capture the essence of quantum theory
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Cited by in corpus (12)

• Semidefinite programming relaxations for quantum correlations
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• Contextuality in anomalous heat flow
• No-broadcasting characterizes operational contextuality
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
• Theory-independent monitoring of the decoherence of a superconducting qubit with generalized contextuality
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• Typicality of Contextuality