Contextuality without incompatibility

Abstract

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable notion of classicality is the existence of a generalized-noncontextual ontological model. In particular, this notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We leverage this fact to demonstrate that measurement incompatibility is neither necessary nor sufficient for proofs of the failure of generalized noncontextuality. Furthermore, we show that every proof of the failure of generalized noncontextuality in a quantum prepare-measure scenario can be converted into a proof of the failure of generalized noncontextuality in a corresponding scenario with no incompatible measurements.

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Cited by in corpus (18)

• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
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• A linear program for testing nonclassicality and an open-source implementation
• Contextuality as a Precondition for Quantum Entanglement
• Contextuality with vanishing coherence and maximal robustness to dephasing
• Testing quantum theory by generalizing 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
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Sufficiency of the counterfactual account of Lüders' rule to rule out ontological models of quantum mechanics
• Minimal operational theories: classical theories with quantum features
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• Measure of set imaginarity
• On compatibility of binary qubit measurements
• Typicality of Contextuality