Jarzynski-like equality for the out-of-time-ordered correlator
- Creators
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Yunger Halpern, Nicole
Abstract
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.
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.Attached Files
Published - PhysRevA.95.012120.pdf
Submitted - 1609.00015v2.pdf
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Additional details
- Eprint ID
- 72729
- Resolver ID
- CaltechAUTHORS:20161212-135444666
- NSF
- PHY-0803371
- Institute for Quantum Information and Matter (IQIM)
- NSF Physics Frontiers Center
- Gordon and Betty Moore Foundation
- Created
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2016-12-12Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter