All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences

Abstract

Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of which has a finite number of outcomes. Given any fixed sets of operational equivalences among the preparations and among the measurements as input, the algorithm returns a set of noncontextuality inequalities whose satisfaction is necessary and sufficient for a set of operational data to admit of a noncontextual model. Additionally, we show that the space of noncontextual data tables always defines a polytope. Finally, we provide a computationally efficient means for testing whether any set of numerical data admits of a noncontextual model, with respect to any fixed operational equivalences. Together, these techniques provide complete methods for characterizing arbitrary noncontextuality scenarios, both in theory and in practice. Because a quantum prepare-and-measure experiment admits of a noncontextual model if and only if it admits of a positive quasiprobability representation, our techniques also determine the necessary and sufficient conditions for the existence of such a representation.

Equation numbering adjusted to match published version. Bibliography updated. Erratum: typographical errors corrected in Eq. (35) [or Eq. (26) in arXiv v2]

References in corpus (16)

• Hidden Variables and the Two Theorems of John Bell
• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• Certified randomness in quantum physics
• Negativity and contextuality are equivalent notions of nonclassicality
• Anomalous Weak Values Are Proofs of Contextuality
• Preparation contextuality powers parity-oblivious multiplexing
• Computational power of correlations
• Information-Theoretic Implications of Quantum Causal Structures
• The contextual fraction as a measure of contextuality
• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Extremal correlations of the tripartite no-signaling polytope
• Partial list of bipartite Bell inequalities with four binary settings
• Fine's theorem, noncontextuality, and correlations in Specker's scenario
• Parity Oblivious d-Level Random Access Codes and Class of Noncontextuality Inequalities
• A linear program for testing local realism

Cited by in corpus (47)

• Kochen-Specker Contextuality
• Anomalous weak values and contextuality: robustness, tightness, and imaginary parts
• The Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Why interference phenomena do not capture the essence of quantum theory
• Uniqueness of noncontextual models for stabilizer subtheories
• Aspects of the phenomenology of interference that are genuinely nonclassical
• Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers
• Resource theory of contextuality for arbitrary prepare-and-measure experiments
• What is nonclassical about uncertainty relations?
• Characterising and bounding the set of quantum behaviours in contextuality scenarios
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Contextuality of general probabilistic theories
• Contextuality without incompatibility
• A structure theorem for generalized-noncontextual ontological models
• Coherence and contextuality in a Mach-Zehnder interferometer
• An invertible map between Bell non-local and contextuality scenarios
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Classical Simulation of Noncontextual Pauli Hamiltonians
• Bounding and simulating contextual correlations in quantum theory
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• Contextuality and The Single-Qubit Stabilizer Formalism
• Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario
• A linear program for testing nonclassicality and an open-source implementation
• Contextuality as a Precondition for Quantum Entanglement
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Contextuality with vanishing coherence and maximal robustness to dephasing
• Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
• Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states
• Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios
• Incompatibility in restricted operational theories: connecting contextuality and steering
• Geometry of joint reality: device-independent steering and operational completeness
• Contextuality in anomalous heat flow
• Contextuality without access to a tomographically complete set
• No-broadcasting characterizes operational contextuality
• Quantitative relations between different measurement contexts
• Contextuality witness inspired by optimal state discrimination
• Revealing quantum contextuality using a single measurement device
• Tracing quantum correlations back to collective interferences
• Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
• Emergence of noncontextuality under quantum Darwinism
• Sufficiency of the counterfactual account of Lüders' rule to rule out ontological models of quantum mechanics
• Contextual advantages across two-state discrimination strategies
• Partial ignorance communication tasks in quantum theory
• On random classical marginal problems with applications to quantum information theory
• Typicality of Contextuality