Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables

Abstract

Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions) metrology (standard and post-selected), thermodynamics (power output and fluctuation theorems), foundations (contextuality, anomalous weak values) and more. Given the growing relevance of the KDQ across the quantum sciences, our aim is two-fold: First, we highlight the role played by quasiprobabilities in characterizing the statistics of quantum observables and processes in the presence of measurement incompatibility. In this way, we show how the KDQ naturally underpins and unifies quantum correlators, quantum currents, Loschmidt echoes, and weak values. Second, we provide novel theoretical and experimental perspectives by discussing a wide variety of schemes to access the KDQ and its non-classicality features.

31+4 pages, 6 figures. V3 accepted for publication in Quantum

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• 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
• Exploring quasiprobability approach to quantum work in the presence of initial coherence: Advantages of the Margenau-Hill distribution
• Interferometry of quantum correlation functions to access quasiprobability distribution of work
• Non-Abelian transport distinguishes three usually equivalent notions of entropy production
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• Characterizing the geometry of the Kirkwood-Dirac positive states
• Quantum speed limit for Kirkwood-Dirac quasiprobabilities
• Dimension-independent weak value estimation via controlled SWAP operations
• Kirkwood-Dirac classical pure states
• Contextuality in anomalous heat flow
• Snapshotting Quantum Dynamics at Multiple Time Points
• Quantum unital Otto heat engines: using Kirkwood-Dirac quasi-probability for the engine's coherence to stay alive
• Convex roofs witnessing Kirkwood-Dirac nonpositivity
• Energetics of Fano coherence generation
• Multipartite quantum states over time from two fundamental assumptions
• Compatibility of Quantum Measurements and the Emergence of Classical Objectivity
• Quasiprobability distributions with weak measurements
• Non-positive energy quasidistributions in coherent collision models
• 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
• Experimental demonstration of generalized quantum fluctuation theorems in the presence of coherence
• Statistical signatures of quantum contextuality
• Contextuality Can be Verified with Noncontextual Experiments
• Work fluctuation theorems with initial quantum coherence
• Quasiprobability Thermodynamic Uncertainty Relation
• Impact of quantum coherence on the dynamics and thermodynamics of quenched free fermions coupled to a localized defect
• Excited stated quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model
• The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity
• Quasi-probability distribution of work in a measurement-based quantum Otto engine
• Energy exchange statistics and fluctuation theorem for non-thermal asymptotic states
• Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
• Coherent heat exchange in a prethermalizing open quantum system
• Quantum Coherence and Anomalous Work Extraction in Qubit Gate Dynamics
• Estimation of multivariate traces of states given partial classical information
• Universal Statistics of Charges Exchanges in Non-Abelian Quantum Transport
• Quantum advantage from negativity of a work quasiprobability distribution
• Quantum Non-Demolition Measurements and Leggett-Garg inequality
• Hermitian Kirkwood-Dirac real operators for discrete Fourier transformations
• Almost no experiments have classical Kirkwood-Dirac representations
• Orthogonalization speed-up from quantum coherence after a sudden quench
• Quantum coherence and negative quasi probabilities in a contextual three-path interferometer