From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities

Abstract

The Kochen-Specker theorem rules out models of quantum theory wherein projective measurements are assigned outcomes deterministically and independently of context. This notion of noncontextuality is not applicable to experimental measurements because these are never free of noise and thus never truly projective. For nonprojective measurements, therefore, one must drop the requirement that an outcome is assigned deterministically in the model and merely require that it is assigned a distribution over outcomes in a manner that is context-independent. By demanding context-independence in the representation of preparations as well, one obtains a generalized principle of noncontextuality that also supports a quantum no-go theorem. Several recent works have shown how to derive inequalities on experimental data which, if violated, demonstrate the impossibility of finding a generalized-noncontextual model of this data. That is, these inequalities do not presume quantum theory and, in particular, they make sense without requiring an operational analogue of the quantum notion of projectiveness. We here describe a technique for deriving such inequalities starting from arbitrary proofs of the Kochen-Specker theorem. It extends significantly previous techniques that worked only for logical proofs, which are based on sets of projective measurements that fail to admit of any deterministic noncontextual assignment, to the case of statistical proofs, which are based on sets of projective measurements that do admit of some deterministic noncontextual assignments, but not enough to explain the quantum statistics.

14 pages, 4 figures, published version

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Cited by in corpus (28)

• Kochen-Specker Contextuality
• All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
• Why interference phenomena do not capture the essence of quantum theory
• Experimentally bounding deviations from quantum theory in the landscape of generalized probabilistic theories
• Uniqueness of noncontextual models for stabilizer subtheories
• Aspects of the phenomenology of interference that are genuinely nonclassical
• Characterising and bounding the set of quantum behaviours in contextuality scenarios
• Contextuality without incompatibility
• Contextuality in entanglement-assisted one-shot classical communication
• Probing the limits of correlations in an indivisible quantum system
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Noncontextuality Inequalities from Antidistinguishability
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• 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
• Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios
• Joint measurability structures realizable with qubit measurements: incompatibility via marginal surgery
• Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
• Quantitative relations between different measurement contexts
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• Revealing quantum contextuality using a single measurement device
• Contextuality witness inspired by optimal state discrimination
• Tracing quantum correlations back to collective interferences
• Emergence of noncontextuality under quantum Darwinism
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory