Negativity and contextuality are equivalent notions of nonclassicality

Abstract

Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and (ii) contextuality, that is, the impossibility of a noncontextual hidden variable model of quantum theory (also known as the Bell-Kochen-Specker theorem). Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, we demonstrate that they prove inadequate to the task and we argue for a particular way of generalizing and revising them. With the refined version of each in hand, it becomes apparent that they are in fact one and the same. We also demonstrate the impossibility of noncontextuality or nonnegativity in quantum theory with a novel proof that is symmetric in its treatment of measurements and preparations.

5 pages, published version (modulo some supplementary material)

References in corpus (6)

• Contextuality for preparations, transformations, and unsharp measurements
• Nonlocality of Einstein-Podolsky-Rosen State in Wigner Representation
• Quantum states and generalized observables: a simple proof of Gleason's theorem
• Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements
• Bell's Inequality Violation (BIQV) with Non-Negative Wigner Function
• A condition for any realistic theory of quantum systems

Cited by in corpus (214)

• Negative Quasi-Probability as a Resource for Quantum Computation
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Quantum-Bayesian Coherence: The No-Nonsense Version
• Non-Gaussian Quantum States and Where to Find Them
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Anomalous Weak Values Are Proofs of Contextuality
• An experimental test of noncontextuality without unwarranted idealizations
• Quasi-probability representations of quantum theory with applications to quantum information science
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• The completeness of quantum theory for predicting measurement outcomes
• Quasi-quantization: classical statistical theories with an epistemic restriction
• Quantum from principles
• Non-Gaussian quantum states of a multimode light field
• The quasiprobability behind the out-of-time-ordered correlator
• Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction
• Wigner function negativity and contextuality in quantum computation on rebits
• Quantum Advantage in Postselected Metrology
• Weak Values are Interference Phenomena
• Contextual advantage for state discrimination
• Contextuality and Wigner function negativity in qubit quantum computation
• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Quantum fluctuation theorems, contextuality and work quasi-probabilities
• Observing Dirac's classical phase space analog to the quantum state
• Reformulating and Reconstructing Quantum Theory
• Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
• Non-classicality criteria from phase-space representations and information-theoretical constraints are maximally inequivalent
• From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism
• A quasiprobability distribution for heat fluctuations in the quantum regime
• Memory cost of quantum contextuality
• Equivalence between contextuality and negativity of the Wigner function for qudits
• Visualizing operators of coupled spin systems
• Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• The Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories
• The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory
• Kirkwood-Dirac nonclassicality, support uncertainty and complete incompatibility
• Efficient classical simulation of matchgate circuits with generalized inputs and measurements
• Fluctuation Theorems for a Quantum Channel
• All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Contextual-value approach to the generalized measurement of observables
• Why interference phenomena do not capture the essence of quantum theory
• Conditions tighter than noncommutation needed for nonclassicality
• Uniqueness of noncontextual models for stabilizer subtheories
• Communication games reveal preparation contextuality
• Quantum Advantage from Sequential-Transformation Contextuality
• Axiomatic and operational connections between the $l_1$-norm of coherence and negativity
• Quasiprobability representations of quantum mechanics with minimal negativity
• Quasiprobability representation of quantum coherence
• Notes on general SIC-POVMs
• Properties and Applications of the Kirkwood-Dirac Distribution
• Quantification and manipulation of magic states
• Aspects of the phenomenology of interference that are genuinely nonclassical
• Negative Conditional Entropy of Post-Selected States
• Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers
• Entropic uncertainty relations for quantum information scrambling
• Quasiprobabilities in quantum thermodynamics and many-body systems
• Quasi-probability distributions for observables in dynamic systems
• Necessity of negativity in quantum theory
• Nonnegative subtheories and quasiprobability representations of qubits
• Phase-space inequalities beyond negativities
• Nonlinearity as a resource for nonclassicality in anharmonic systems
• Nonclassicality of states and measurements by breaking classical bounds on statistics
• Witnessing Wigner Negativity
• Using weak values to experimentally determine "negative probabilities" in a two-photon state with Bell correlations
• Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
• Measures of Contextuality and Noncontextuality
• Quasiprobability distributions for quantum-optical coherence and beyond
• Noise-robust preparation contextuality shared between any number of observers via unsharp measurements
• Discrete Wigner Formalism for Qubits and Non-Contextuality of Clifford Gates on Qubit Stabilizer States
• Conditional Hybrid Nonclassicality
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Causation does not explain contextuality
• Quantum-Bayesian Coherence
• Contextuality of general probabilistic theories
• Quantum phase-space representation for curved configuration spaces
• Contextuality without incompatibility
• Probability representation of quantum dynamics using pseudostochastic maps
• Minimizing back-action through entangled measurements
• Common Denominator for Value and Expectation No-Go Theorems
• A structure theorem for generalized-noncontextual ontological models
• Heterodyne photodetection measurements on cavity optomechanical systems: Interpretation of sideband asymmetry and limits to a classical explanation
• Quantum information in the Posner model of quantum cognition
• Mesoscopic ultrafast nonlinear optics -- The emergence of multimode quantum non-Gaussian physics
• Interferometry of quantum correlation functions to access quasiprobability distribution of work
• Inequalities witnessing coherence, nonlocality, and contextuality
• Classical Simulation of Noncontextual Pauli Hamiltonians
• Tunnelling necessitates negative Wigner function
• Quasiprobability distribution of work in the quantum Ising model
• Bounding Quantum Advantages in Postselected Metrology
• 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
• Negativity Bounds for Weyl-Heisenberg Quasiprobability Representations
• The role of cohomology in quantum computation with magic states
• State-injection schemes of quantum computation in Spekkens' toy theory
• Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario
• The classical-quantum limit
• Time evolution of coupled spin systems in a generalized Wigner representation
• Some Examples of Contextuality in Physics: Implications to Quantum Cognition
• Quasistates and quasiprobabilities
• A linear program for testing nonclassicality and an open-source implementation
• Approximate stabilizer rank and improved weak simulation of Clifford-dominated circuits for qudits
• Contextuality with vanishing coherence and maximal robustness to dephasing
• Contextual Subspace Variational Quantum Eigensolver Calculation of the Dissociation Curve of Molecular Nitrogen on a Superconducting Quantum Computer
• Quantum space-time marginal problem: global causal structure from local causal information
• The magic of universal quantum computing with permutations
• A review and reformulation of macroscopic realism: resolving its deficiencies using the framework of generalized probabilistic theories
• Testing quantum theory by generalizing noncontextuality
• On the role of joint probability distributions of incompatible observables in Bell and Kochen-Specker Theorems
• Anomalous energy exchanges and Wigner function negativities in a single qubit gate
• Quantum Theory is a Quasi-stochastic Process Theory
• Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance
• Epistemically restricted phase space representation, weak momentum value, and reconstruction of quantum wave function
• Minimal informationally complete measurements for probability representation of quantum dynamics
• Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states
• Contextuality, Fine-Tuning, and Teleological Explanation
• Certifying Non-Classical Behavior for Negative Keldysh Quasi-Probabilities
• Economical ontological models for discrete quantum systems
• Optical experiment to test negative probability in context of quantum-measurement selection
• The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
• Universal resources for quantum computing
• Semiclassical Formulation of Gottesman-Knill and Universal Quantum Computation
• Constructing Squeezed States of Light with Associated Hermite Polynomials
• Multi-time correlations in the positive-P, Q, and doubled phase-space representations
• Quantum speed limit for Kirkwood-Dirac quasiprobabilities
• Phase-space negativity as a computational resource for quantum kernel methods
• Contextuality beyond the Kochen-Specker theorem
• Measuring Observable Quantum Contextuality
• Contextuality in anomalous heat flow
• Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits
• Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
• Geometry of joint reality: device-independent steering and operational completeness
• Angular-momentum nonclassicality by breaking classical bounds on statistics
• Snapshotting Quantum Dynamics at Multiple Time Points
• No-broadcasting characterizes operational contextuality
• Heralded processes on continuous-variable spaces as quantum maps
• Measurement Contextuality and Planck's Constant
• Non-Classical Kernels in Continuous Variable Systems
• Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation
• A classical formulation of quantum theory?
• From reasonable postulates to generalised Hamiltonian systems
• Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
• Quantum Bochner's theorem for phase spaces built on projective representations
• The Minimal Modal Interpretation of Quantum Theory
• Six-dimensional light-front Wigner distribution of hadrons
• Contextuality witness inspired by optimal state discrimination
• Playing nonlocal games with phases of quantum matter
• A multi-player, multi-team nonlocal game for the toric code
• Projecting onto any two-photon polarization state using linear optics
• Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit
• Energetics of Fano coherence generation
• On reconciling quantum mechanics and local realism
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• Inequalities for complementarity in observed statistics
• Orbital-Free Quasi-Density Functional Theory
• Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Nonclassical correlations of radiation in relation to Bell nonlocality
• Hidden variable model for quantum computation with magic states on qudits of any dimension
• Entanglement and Quantum Superposition of a Macroscopic - Macroscopic system
• Logical Entropy and Negative Probabilities in Quantum Mechanics
• Spekkens's Symmetric No-Go Theorem
• Quantum entanglement as an extremal Kirkwood-Dirac nonreality
• Optimizing single-photon quantum radar detection through partially postselected filtering
• Geometry of Kirkwood-Dirac classical states: A case study based on discrete Fourier transform
• Leggett-Garg test of macrorealism using indefinite causal order of measurements
• Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
• Separation of measurement uncertainty into quantum and classical parts based on Kirkwood-Dirac quasiprobability and generalized entropy
• Wigner and friends, a map is not the territory! Contextuality in multi-agent paradoxes
• Tracing quantum correlations back to collective interferences
• The violation of Bell-CHSH inequalities leads to different conclusions depending on the description used
• Statistical signatures of quantum contextuality
• Quasiprobability Thermodynamic Uncertainty Relation
• Harvesting Contextuality from the Vacuum
• Analysis of single-particle nonlocality through the prism of weak measurements
• On Hidden Variables: Value and Expectation No-Go Theorems
• On measures of classicality/quantumness in quasiprobability representations of finite-dimensional quantum systems
• Noise-adaptive test of quantum correlations with quasiprobability functions
• Contextuality Can be Verified with Noncontextual Experiments
• Emergence of noncontextuality under quantum Darwinism
• A Bayesian quasi-probability approach to inferring the past of quantum observables
• Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
• Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations
• Theory-independent monitoring of the decoherence of a superconducting qubit with generalized contextuality
• Quantum conditional probabilities
• Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
• Interference Energy Spectrum of the Infinite Square Well
• Entanglement and magic on the light-front
• Quantum computational advantage implies contextuality
• Nonclassicality of induced coherence witnessed by contextuality
• Twenty years of quantum contextuality at USTC
• The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity
• Differential Geometry of Contextuality
• Deterministic Gaussian conversion protocols for non-Gaussian single-mode resources
• Generalized Gleason theorem and finite amount of information for the context
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• Typicality of Contextuality
• Almost no experiments have classical Kirkwood-Dirac representations
• Ideal stochastic process modeling with post-quantum quasiprobabilistic theories
• Dynamics of nonclassicality in a generalized Tavis Cummings model with XY spin $(1/2,1)$ atomic interactions
• Advantage in two-way communication using non-classical states of light
• All fundamental non-contextuality inequalities are unique
• Noncontextual Pauli Hamiltonians
• Efficient measure of information backflow with a quasistochastic process
• Common Denominator for Value and Expectation No-go Theorems: Extended Abstract
• Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables
• Contextuality from the vacuum
• Photon triplets from integrated microrings: A path towards deterministic non-Gaussianity on a chip
• Joint quasiprobability distribution on the measurement outcomes of MUB-driven operators
• Limitations imposed by complementarity
• Indistinguishability and Negative Probabilities
• Quantum vs. noncontextual semi-device-independent randomness certification
• Operational quasiprobabilities for continuous variables