Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario

Abstract

Starting from arbitrary sets of quantum states and measurements, referred to as the prepare-and-measure scenario, an operationally noncontextual ontological model of the quantum statistics associated with the prepare-and-measure scenario is constructed. The operationally noncontextual ontological model coincides with standard Spekkens noncontextual ontological models for tomographically complete scenarios, while covering the non-tomographically complete case with a new notion of a reduced space, which we motivate following the guiding principles of noncontextuality. A mathematical criterion, called unit separability, is formulated as the relevant classicality criterion -- the name is inspired by the usual notion of quantum state separability. Using this criterion, we derive a new upper bound on the cardinality of the ontic space. Then, we recast the unit separability criterion as a (possibly infinite) set of linear constraints, from which we obtain two separate hierarchies of algorithmic tests to witness the non-classicality or certify the classicality of a scenario. Finally, we reformulate our results in the framework of generalized probabilistic theories and discuss the implications for simplex-embeddability in such theories.

arXiv comment18 + 30 pages. V4: updated to match journal version

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Cited by in corpus (11)

• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
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• A structure theorem for generalized-noncontextual ontological models
• Contextuality as a Precondition for Quantum Entanglement
• A linear program for testing nonclassicality and an open-source implementation
• Testing quantum theory by generalizing noncontextuality
• Incompatibility in restricted operational theories: connecting contextuality and steering
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• Theory-independent monitoring of the decoherence of a superconducting qubit with generalized contextuality
• Quantum description of reality is epistemically incomplete