The quasiprobability behind the out-of-time-ordered correlator

Abstract

Two topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC has been shown to equal a moment of a summed quasiprobability. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze the weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.

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References in corpus (27)

• Black holes as mirrors: quantum information in random subsystems
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Experimental Comparison of Two Quantum Computing Architectures
• Progressive field-state collapse and quantum non-demolition photon counting
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Negativity and contextuality are equivalent notions of nonclassicality
• Detecting bit-flip errors in a logical qubit using stabilizer measurements
• Anomalous Weak Values Are Proofs of Contextuality
• The role of quantum measurement in stochastic thermodynamics
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Quantum chaos on a critical Fermi surface
• Measurement of many-body chaos using a quantum clock
• Dynamics of simultaneously measured non-commuting observables
• Jarzynski-like equality for the out-of-time-ordered correlator
• Onset of many-body chaos in the $O(N)$ model
• Wigner function negativity and contextuality in quantum computation on rebits
• Weak Values are Interference Phenomena
• Quantum butterfly effect in weakly interacting diffusive metals
• Compressive Direct Measurement of the Quantum Wave Function
• Resilience of scrambling measurements
• Probing Quantum Interference Effects in the Work Distribution
• Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
• Quasi-probability distributions for observables in dynamic systems
• Compressive Wavefront Sensing with Weak Values
• Comment on: How the result of a single coin toss can turn out to be 100 heads
• On Quantisations, Quasi-probabilities and the Weak Value

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• Dynamical Scaling Laws of Out-of-Time-Ordered Correlators
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Non-Abelian transport distinguishes three usually equivalent notions of entropy production
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• Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach
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