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Separation of Out-Of-Time-Ordered Correlation and Entanglement

Harrow, Aram W. and Kong, Linghang and Liu, Zi-Wen and Mehraban, Saeed and Shor, Peter W. (2021) Separation of Out-Of-Time-Ordered Correlation and Entanglement. PRX Quantum, 2 (2). Art. No. 020339. ISSN 2691-3399. doi:10.1103/PRXQuantum.2.020339.

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The out-of-time-ordered correlation (OTOC) and entanglement are two physically motivated and widely used probes of the “scrambling” of quantum information, a phenomenon that has drawn great interest recently in quantum gravity and many-body physics. We argue that the corresponding notions of scrambling can be fundamentally different, by proving an asymptotic separation between the time scales of the saturation of OTOC and that of entanglement entropy in a random quantum-circuit model defined on graphs with a tight bottleneck, such as tree graphs. Our result counters the intuition that a random quantum circuit mixes in time proportional to the diameter of the underlying graph of interactions. It also provides a more rigorous justification for an argument in our previous work [Shor P.W., Scrambling time and causal structure of the photon sphere of a Schwarzschild black hole, arXiv:1807.04363 (2018)], that black holes may be slow information scramblers, which in turn relates to the black-hole information problem. The bounds we obtain for OTOC are interesting in their own right in that they generalize previous studies of OTOC on lattices to the geometries on graphs in a rigorous and general fashion.

Item Type:Article
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URLURL TypeDescription Paper
Harrow, Aram W.0000-0003-3220-7682
Kong, Linghang0000-0002-5854-5340
Liu, Zi-Wen0000-0002-3402-9763
Additional Information:© 2021 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 11 October 2019; revised 22 December 2020; accepted 4 May 2021; published 11 June 2021. A.W.H. is funded by NSF Grants No. CCF-1452616, No. CCF-1729369, and No. PHY-1818914; ARO contract W911NF-17-1-0433; and the MIT-IBM Watson AI Lab under the project Machine Learning in Hilbert space. Z.W.L. is supported by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. L.K. is funded by NSF grant CCF-1452616. S.M. is funded by NSF Grant No. CCF-1729369. P.W.S. is supported by the National Science Foundation under Grants No. CCF-1525130 and No. CCF-1729369 and through the NSF Science and Technology Center for Science of Information under Grant No. CCF-0939370.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-17-1-0433
Massachusetts Institute of Technology (MIT)UNSPECIFIED
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Industry CanadaUNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20210622-220353587
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109540
Deposited By: Tony Diaz
Deposited On:23 Jun 2021 18:44
Last Modified:23 Jun 2021 18:44

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