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Jarzynski-like equality for the out-of-time-ordered correlator

Yunger Halpern, Nicole (2017) Jarzynski-like equality for the out-of-time-ordered correlator. Physical Review A, 95 (1). Art. No. 012120. ISSN 1050-2947. doi:10.1103/PhysRevA.95.012120.

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The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation relations such as Jarzynski's equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a Jarzynski-like equality for the OTOC. The equality's left-hand side equals the OTOC. The right-hand side suggests a protocol for measuring the OTOC indirectly. The protocol is platform-nonspecific and can be performed with weak measurement or with interference. Time evolution need not be reversed in any interference trial. The equality enables fluctuation relations to provide insights into holography, condensed matter, and quantum information and vice versa.

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Yunger Halpern, Nicole0000-0001-8670-6212
Additional Information:© 2017 American Physical Society. Received 1 September 2016; published 17 January 2017. I have the pleasure of thanking Fernando G. S. L. Brandão, Jordan S. Cotler, David Ding, Yichen Huang, Geoff Penington, Evgeny Mozgunov, Brian Swingle, Christopher D. White, and Yong-Liang Zhang for valuable discussions. I am grateful to Justin Dressel for sharing weak-measurement and quasiprobability expertise, to Sebastian Deffner and John Goold for discussing fluctuation relations' forms, to Alexey Gorshkov for sharing interference expertise, to Alexei Kitaev for introducing me to the OTOC during Ph 219c preparations, to John Preskill for suggesting combining the OTOC with fluctuation relations, and to Norman Yao for spotlighting degeneracies. This research was supported by National Science Foundation (NSF) Grant No. PHY-0803371. The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center supported by the Gordon and Betty Moore Foundation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:1
Classification Code:PACS numbers: 05.45.Mt 03.67.-a 05.70.Ln, 05.30.-d
Record Number:CaltechAUTHORS:20161212-135444666
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72729
Deposited By: Ruth Sustaita
Deposited On:12 Dec 2016 23:15
Last Modified:11 Nov 2021 05:05

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