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Quasiprobability behind the out-of-time-ordered correlator

Yunger Halpern, Nicole and Swingle, Brian and Dressel, Justin (2018) Quasiprobability behind the out-of-time-ordered correlator. Physical Review A, 97 (4). Art. No. 042105. ISSN 2469-9926. doi:10.1103/PhysRevA.97.042105.

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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 was shown to equal a moment of a summed quasiprobability [Yunger Halpern, Phys. Rev. A 95, 012120 (2017)]. 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 Yunger Halpern's 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. We define an extended KD quasiprobability that generalizes the KD distribution. 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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Yunger Halpern, Nicole0000-0001-8670-6212
Additional Information:© 2018 American Physical Society. Received 13 April 2017; published 10 April 2018. This research was supported by NSF Grant No. PHY-0803371. Partial financial support came from the Walter Burke Institute for Theoretical Physics at Caltech. The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center supported by the Gordon and Betty Moore Foundation. N.Y.H. thanks J. Cotler and P. Solinas for pointing out the parallel with [108,109]; D. Ding for asking whether A_ρ represents a state; M. Rangamani for discussing K-fold OTOCs; M. Campisi, S. Gazit, J. Goold, J. Jones, L. S. Martin, O. Painter, and N. Yao for discussing experiments; and C. D. White and E. Crosson for discussing computational complexity. Parts of this paper were developed while N.Y.H. was visiting the Stanford ITP and UCL. B.G.S. is supported by the Simons Foundation, as part of the It From Qubit collaboration; through a Simons Investigator Award to S. Todadri; and by MURI Grant No. W911NF-14-1-0003 from ARO. J.D. is supported by ARO Grant No. W911NF-15-1-0496.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Simons FoundationUNSPECIFIED
Army Research Office (ARO)W911NF-14-1-0003
Army Research Office (ARO)W911NF-15-1-0496
Issue or Number:4
Record Number:CaltechAUTHORS:20171108-145509877
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83084
Deposited By: Bonnie Leung
Deposited On:08 Nov 2017 23:06
Last Modified:15 Nov 2021 19:55

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