Measurement incompatibility and steering are necessary and sufficient for operational contextuality

Abstract

Contextuality is a signature of operational nonclassicality in the outcome statistics of an experiment. This notion of nonclassicality applies to a breadth of physical phenomena. Here, we establish its relation to two fundamental nonclassical entities in quantum theory; measurement incompatibility and steering. We show that each is necessary and sufficient the failure of operational contextuality. We exploit the established connection to contextuality to provide a novel approach to problems in measurement incompatibility and steering.

arXiv commentA. T. and R. U. contributed equally to this work

References in corpus (35)

• Bell nonlocality
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Contextuality for preparations, transformations, and unsharp measurements
• Contextuality supplies the magic for quantum computation
• Quantum steering: a review with focus on semidefinite programming
• Einstein, incompleteness, and the epistemic view of quantum states
• Quantum states and generalized observables: a simple proof of Gleason's theorem
• Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
• Contextuality in Measurement-based Quantum Computation
• Anomalous Weak Values Are Proofs of Contextuality
• An Invitation to Quantum Incompatibility
• Joint measurability of generalized measurements implies classicality
• An experimental test of noncontextuality without unwarranted idealizations
• Preparation contextuality powers parity-oblivious multiplexing
• Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
• One-to-one mapping between steering and joint measurability problems
• Improving zero-error classical communication with entanglement
• Contextuality as a resource for models of quantum computation on qubits
• Quantifying quantum resources with conic programming
• Wigner function negativity and contextuality in quantum computation on rebits
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Contextual advantage for state discrimination
• Quantum Incompatibility Witnesses
• Maximally epistemic interpretations of the quantum state and contextuality
• Optimal bounds for parity-oblivious random access codes
• Quantum measurement incompatibility does not imply Bell nonlocality
• Measurement incompatibility does not give rise to Bell violation in general
• Nonlocality of a single photon: paths to an EPR-steering experiment
• Communication games reveal preparation contextuality
• Most incompatible measurements for robust steering tests
• Preparation contextuality as an essential feature underlying quantum communication advantage
• Adaptive strategy for joint measurements
• Robust preparation noncontextuality inequalities in the simplest scenario
• Spatial versus Sequential Correlations for Random Access Coding
• Distributed sampling, quantum communication witnesses, and measurement incompatibility

Cited by in corpus (47)

• Kochen-Specker Contextuality
• Certifying quantum signatures in thermodynamics and metrology via contextuality of quantum linear response
• Experimental characterisation of unsharp qubit observables and sequential measurement incompatibility via quantum random access codes
• Set coherence: basis-independent quantification of quantum coherence
• Contextual advantage for state-dependent cloning
• Complete classification of steerability under local filters and its relation with measurement incompatibility
• Noise-robust preparation contextuality shared between any number of observers via unsharp measurements
• Quantification of quantum dynamics with input-output games
• Contextuality without incompatibility
• Quantum marginal problem and incompatibility
• Contextuality in entanglement-assisted one-shot classical communication
• Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness
• Quantum Contextuality
• Operational nonclassicality in minimal autonomous thermal machines
• Measuring incompatibility and clustering quantum observables with a quantum switch
• An invertible map between Bell non-local and contextuality scenarios
• Bounding and simulating contextual correlations in quantum theory
• Device-independent quantification of measurement incompatibility
• Device-independent self-testing of unsharp measurements
• Widening the sharpness modulation region of an entanglement-assisted sequential quantum random access code: Theory, experiment, and application
• Contextuality as a Precondition for Quantum Entanglement
• Quantum measurement incompatibility in subspaces
• General Method for Classicality Certification in the Prepare and Measure Scenario
• Characterizing and quantifying the incompatibility of quantum instruments
• Incompatibility in restricted operational theories: connecting contextuality and steering
• Role of fine-grained uncertainty in determining the limit of preparation contextuality
• No-broadcasting characterizes operational contextuality
• Incompatibility of quantum instruments
• Self-testing of multiple unsharpness parameters through sequential violations of non-contextual inequality
• Automated Generation of Arbitrarily Many Kochen-Specker and Other Contextual Sets in Odd Dimensional Hilbert Spaces
• 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
• Naimark dilations of qubit POVMs and joint measurements
• Tsirelson inequalities: Detecting cheating and quantumness in a single framework
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Non-Kochen-Specker Contextuality
• Contextual quantum metrology
• Compressing continuous variable quantum measurements
• Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications
• Symmetries and Wigner representations of operational theories
• Partial ignorance communication tasks in quantum theory
• Resource theory of interactive quantum instruments
• Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
• Semi-device-independent certification of number of measurements
• On compatibility of binary qubit measurements
• Robust device-independent characterization of sharpness and incompatibility of unsharp instruments
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory