Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra

Abstract

Weak values and Kirkwood--Dirac (KD) quasiprobability distributions have been independently associated with both foundational issues in quantum theory and advantages in quantum metrology. We propose simple quantum circuits to measure weak values, KD distributions, and spectra of density matrices without the need for post-selection. This is achieved by measuring unitary-invariant, relational properties of quantum states, which are functions of Bargmann invariants, the concept that underpins our unified perspective. Our circuits also enable experimental implementation of various functions of KD distributions, such as out-of-time-ordered correlators (OTOCs) and the quantum Fisher information in post-selected parameter estimation, among others. An upshot is a unified view of nonclassicality in all those tasks. In particular, we discuss how negativity and imaginarity of Bargmann invariants relate to set coherence.

27+6 pages, 7+5 figures. v2: new sections 2.3, 2.4, 3, 4.5, revised structure. v3: improved section 5, added references. Comments are welcome!

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Cited by in corpus (42)

• 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
• Nonlocal Advantages of Quantum Imaginarity
• Interferometry of quantum correlation functions to access quasiprobability distribution of work
• Shallow unitary decompositions of quantum Fredkin and Toffoli gates for connectivity-aware equivalent circuit averaging
• Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
• Characterizing the geometry of the Kirkwood-Dirac positive states
• Quantifying imaginarity in terms of pure-state imaginarity
• Dimension-independent weak value estimation via controlled SWAP operations
• Quantum speed limit for Kirkwood-Dirac quasiprobabilities
• Kirkwood-Dirac classical pure states
• Spacetime quantum and classical mechanics with dynamical foliation
• Contextuality in anomalous heat flow
• Counterfactuality, back-action, and information gain in multi-path interferometers
• Geometry of sets of Bargmann invariants
• Energetics of Fano coherence generation
• Certifying nonstabilizerness in quantum processors
• Non-positive energy quasidistributions in coherent collision models
• Compatibility of Quantum Measurements and the Emergence of Classical Objectivity
• 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
• Geometry of Kirkwood-Dirac classical states: A case study based on discrete Fourier transform
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Imaginarity measures induced by real part states and the complementarity relations
• Statistical signatures of quantum contextuality
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation
• 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
• Resource-efficient algorithm for estimating the trace of quantum state powers
• Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
• An Elementary Characterization of Bargmann Invariants
• Digital Quantum Simulations of the Non-Resonant Open Tavis-Cummings Model
• Experimental certification of the nonlocal advantages of quantum imaginarity
• Quantum Non-Demolition Measurements and Leggett-Garg inequality
• Hermitian Kirkwood-Dirac real operators for discrete Fourier transformations
• Estimation of multivariate traces of states given partial classical information
• Quantum coherence and negative quasi probabilities in a contextual three-path interferometer
• Quantum speed limit for observables from quantum asymmetry
• Generalized Numerical Construction of MUBs: A Group Theoretical Investigation
• Measure of set imaginarity