Anomalous Weak Values Are Proofs of Contextuality

Abstract

The average result of a weak measurement of some observable $A$ can, under post-selection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of post-selection and hence possible contribution of measurement-disturbance, has led to a long-running debate about whether or not this is surprising. Here, it is shown that such "anomalous weak values" are non-classical in a precise sense: a sufficiently weak measurement of one constitutes a proof of contextuality. This clarifies, for example, which features must be present (and in an experiment, verified) to demonstrate an effect with no satisfying classical explanation.

arXiv comment4 pages. v2: Some typos fixed and some discussions expanded

References in corpus (20)

• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Contextuality for preparations, transformations, and unsharp measurements
• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Complex weak values in quantum measurement
• Negativity and contextuality are equivalent notions of nonclassicality
• Violation of the Leggett-Garg inequality with weak measurements of photons
• Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values
• Weak values and the Leggett-Garg inequality in solid-state qubits
• Experimental Realization of the Quantum Box Problem
• Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements
• Quantum Cheshire Cats
• Observation of a quantum Cheshire Cat in a matter wave interferometer experiment
• Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction
• How the result of a single coin toss can turn out to be 100 heads
• Photon trajectories, anomalous velocities, and weak measurements: A classical interpretation
• The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory
• Contextual-value approach to the generalized measurement of observables
• Pre- and post-selection, weak values, and contextuality
• Classical Field Approach to Quantum Weak Measurements
• The Uncertainty Relation in "Which-Way" Experiments: How to Observe Directly the Momentum Transfer using Weak Values

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• Measuring incompatible observables of a single photon
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• Anomalous weak values and contextuality: robustness, tightness, and imaginary parts
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• Weak-to-strong transition of quantum measurement in a trapped-ion system
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• Quantifying quantum coherence via nonreal Kirkwood-Dirac quasiprobability
• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra
• The Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories
• Experimental demonstration of direct path state characterization by strongly measuring weak values in a matter-wave interferometer
• Experiment Investigating the Connection between Weak Values and Contextuality
• Kirkwood-Dirac nonclassicality, support uncertainty and complete incompatibility
• Measurement incompatibility and steering are necessary and sufficient for operational contextuality
• All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
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• Uniqueness of noncontextual models for stabilizer subtheories
• Communication games reveal preparation contextuality
• The Case of the Disappearing (and Re-Appearing) Particle
• Properties and Applications of the Kirkwood-Dirac Distribution
• Aspects of the phenomenology of interference that are genuinely nonclassical
• Quasi-probability distributions for observables in dynamic systems
• Quasiprobabilities in quantum thermodynamics and many-body systems
• Can Anomalous Amplification be Attained Without Postselection?
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• Anomalous Weak Values and the Violation of a Multiple-measurement Leggett-Garg Inequality
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• Bounding sets of sequential quantum correlations and device-independent randomness certification
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• General complex Spin Weak Values obtained in Matter-Wave Interferometer Experiments
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• Interference experiment, anomalous weak value and Leggett-Garg test of macrorealism
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Quantum current in dissipative systems
• Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds
• How quantum paradoxes originate from the non-classical statistics of physical properties related to each other by half-periodic transformations
• Contextuality without incompatibility
• Confined Contextuality in Neutron Interferometry: Observing the Quantum Pigeonhole Effect
• Quantum coherence as asymmetry from complex weak values
• Minimizing back-action through entangled measurements
• Observing the "quantum Cheshire cat" effect with noninvasive weak measurement
• Simple understanding of quantum weak values
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• Probing finite coarse-grained virtual Feynman histories with sequential weak values
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• Anomalous Weak Values Emerging from Strong Interactions between Light and Matter
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• A review and reformulation of macroscopic realism: resolving its deficiencies using the framework of generalized probabilistic theories
• The future of secure communications: device independence in quantum key distribution
• Testing quantum theory by generalizing noncontextuality
• Anomalous energy exchanges and Wigner function negativities in a single qubit gate
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• Anomalous Weak Values Without Post-Selection
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• Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
• Epistemically restricted phase space representation, weak momentum value, and reconstruction of quantum wave function
• Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves
• Direct experimental test of commutation relation via weak value
• Experimental evaluation of non-classical correlations between measurement outcomes and target observable in a quantum measurement
• A possible solution to the which-way problem of quantum interference
• A Scheme for Performing Strong and Weak Sequential Measurements of Non-commuting Observables
• Disembodiment of arbitrary number of properties in quantum Cheshire cat experiment
• Dimension-independent weak value estimation via controlled SWAP operations
• Quantum speed limit for Kirkwood-Dirac quasiprobabilities
• Kirkwood-Dirac classical pure states
• Contextuality in anomalous heat flow
• Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
• Sequential propagation of a single photon through five measurement contexts in a three-path interferometer
• No-broadcasting characterizes operational contextuality
• Snapshotting Quantum Dynamics at Multiple Time Points
• On the relevance of weak measurements in dissipative quantum systems
• Exploring postselection-induced quantum phenomena with time-bidirectional state formalism
• Interpreting weak value amplification with a toy realist model
• Why protective measurement does not establish the reality of the quantum state
• Obtaining a Single-Photon Weak Value from Experiments using a Strong (Many-Photon) Coherent State
• Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs
• Energetics of Fano coherence generation
• How much time does a photon spend as an atomic excitation before being transmitted?
• Characterizing Kirkwood-Dirac nonclassicality and uncertainty diagram based on discrete Fourier transform
• Revealing quantum contextuality using a single measurement device
• Weak values from path integrals
• Manifestation of pointer state correlations in complex weak values of quantum observables
• Quantum tomography via Non-orthogonal basis and weak values
• Quasiprobability distributions with weak measurements
• Optimal Settings For Amplification And Estimation Of Small Effects In Postselected Ensembles
• Causal reappraisal of the quantum three box paradox
• Construction of State-independent Proofs for Quantum Contextuality
• Revisiting weak values through non-normality
• Tracing quantum correlations back to collective interferences
• Nonclassical oscillations in pre- and post-selected quantum walks
• Geometry of Kirkwood-Dirac classical states: A case study based on discrete Fourier transform
• Quantum entanglement as an extremal Kirkwood-Dirac nonreality
• Separation of measurement uncertainty into quantum and classical parts based on Kirkwood-Dirac quasiprobability and generalized entropy
• The Geometry of Qubit Weak Values
• No contextual advantage in non-paradoxical scenarios of two state vector formalism
• A Contextuality Based Quantum Key Distribution Protocol
• Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
• Contextuality Can be Verified with Noncontextual Experiments
• Non-locality and entanglement in multi-qubit systems from a unified framework
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation
• Quantum contextuality of complementary photon polarizations explored by adaptive input state control
• Contextual quantum metrology
• Separating a particle's mass from its momentum
• Analysis of single-particle nonlocality through the prism of weak measurements
• Weak measurements, non-classicality and negative probability
• Weak values obtained from mass-energy equivalence
• Understanding weak values without new probability theory
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• Weak Value and the Wave-Particle Duality
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• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory