Conditions tighter than noncommutation needed for nonclassicality

Abstract

Kirkwood discovered in 1933, and Dirac discovered in 1945, a representation of quantum states that has undergone a renaissance recently. The Kirkwood-Dirac (KD) distribution has been employed to study nonclassicality across quantum physics, from metrology to chaos to the foundations of quantum theory. The KD distribution is a quasiprobability distribution, a quantum generalization of a probability distribution, which can behave nonclassically by having negative or nonreal elements. Negative KD elements signify quantum information scrambling and potential metrological quantum advantages. Nonreal elements encode measurement disturbance and thermodynamic nonclassicality. KD distributions' nonclassicality has been believed to follow necessarily from noncommutation of operators. We show that noncommutation does not suffice. We prove sufficient conditions for the KD distribution to be nonclassical (equivalently, necessary conditions for it to be classical). We also quantify the KD nonclassicality achievable under various conditions. This work resolves long-standing questions about nonclassicality and may be used to engineer quantum advantages.

5 (+9) pages, 1 figure. Published in J. Phys. A: Mathematical and Theoretical

References in corpus (11)

• Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
• Complex weak values in quantum measurement
• Negativity and contextuality are equivalent notions of nonclassicality
• Anomalous Weak Values Are Proofs of Contextuality
• Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
• Jarzynski-like equality for the out-of-time-ordered correlator
• Weak Values are Interference Phenomena
• Quantum theory of successive projective measurements
• Weak Measurement of Superconducting Qubit Reconciles Incompatible Operators
• Classical versus quantum completeness
• Post-Selection and Counterfactual Communication

Cited by in corpus (39)

• Negative quasiprobabilities enhance phase estimation in quantum-optics experiment
• 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
• Kirkwood-Dirac nonclassicality, support uncertainty and complete incompatibility
• Properties and Applications of the Kirkwood-Dirac Distribution
• Quasiprobabilities in quantum thermodynamics and many-body systems
• Unitary-invariant witnesses of quantum imaginarity
• Projective measurements can probe non-classical work extraction and time-correlations
• Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds
• Work statistics, quantum signatures and enhanced work extraction in quadratic fermionic models
• Measuring incompatibility and clustering quantum observables with a quantum switch
• Non-Abelian transport distinguishes three usually equivalent notions of entropy production
• Interferometry of quantum correlation functions to access quasiprobability distribution of work
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• Characterizing the geometry of the Kirkwood-Dirac positive states
• General quantum correlation from nonreal values of Kirkwood-Dirac quasiprobability over orthonormal product bases
• Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves
• Quantum speed limit for Kirkwood-Dirac quasiprobabilities
• Kirkwood-Dirac classical pure states
• Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
• On Kirkwood--Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame
• Snapshotting Quantum Dynamics at Multiple Time Points
• Convex roofs witnessing Kirkwood-Dirac nonpositivity
• Energetics of Fano coherence generation
• Characterizing Kirkwood-Dirac nonclassicality and uncertainty diagram based on discrete Fourier transform
• Uncertainty relations for the support of quantum states
• Quasiprobability distributions with weak measurements
• Separation of measurement uncertainty into quantum and classical parts based on Kirkwood-Dirac quasiprobability and generalized entropy
• Geometry of Kirkwood-Dirac classical states: A case study based on discrete Fourier transform
• Contextuality Can be Verified with Noncontextual Experiments
• Impact of quantum coherence on the dynamics and thermodynamics of quenched free fermions coupled to a localized defect
• Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
• Numerical ranges of Bargmann invariants
• The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity
• Almost no experiments have classical Kirkwood-Dirac representations
• Commutativity and the emergence of classical objectivity
• Quantum Non-Demolition Measurements and Leggett-Garg inequality
• Hermitian Kirkwood-Dirac real operators for discrete Fourier transformations