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Entropic uncertainty relations for quantum information scrambling

Yunger Halpern, Nicole and Bartolotta, Anthony and Pollack, Jason (2019) Entropic uncertainty relations for quantum information scrambling. Communications Physics, 2 . Art. No. 92. ISSN 2399-3650.

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Different fields of physics characterize differently how much two quantum operations disagree: quantum information theory features uncertainty relations cast in terms of entropies. The higher an uncertainty bound, the less compatible the operations. In condensed matter and high-energy physics, initially localized, far-apart operators come to disagree as entanglement spreads through a quantum many-body system. This spread, called “scrambling,” is quantified with the out-of-time-ordered correlator (OTOC). We unite these two measures of operation disagreement by proving entropic uncertainty relations for scrambling. The uncertainty bound depends on the quasiprobability (the nonclassical generalization of a probability) known to average to the OTOC. The quasiprobability strengthens the uncertainty bound, we find, when a spin chain scrambles in numerical simulations. Hence our entropic uncertainty relations reflect the same incompatibility as scrambling, uniting two fields’ notions of quantum-operation disagreement.

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Yunger Halpern, Nicole0000-0001-8670-6212
Pollack, Jason0000-0003-4754-4905
Alternate Title:Reconciling two notions of quantum operator disagreement: Entropic uncertainty relations and information scrambling, united through quasiprobabilities
Additional Information:© 2019 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit Received 10 August 2018; Accepted 31 May 2019; Published 07 August 2019. Data availability: The simulation data and code are available at ( We are grateful for conversations with Fernando G. S. L. Brandão, Sean Carroll, Justin Dressel, Patrick Hayden, José Raúl Gonzalez Alonso, Renato Renner, Brian Swingle, and Marco Tomamichel. N.Y.H. is grateful for support from the Institute for Quantum Information and Matter (IQIM), for a Barbara Groce Graduate Fellowship, and for a Graduate Fellowship from the Kavli Institute for Theoretical Physics. N.Y.H. acknowledges Mark van Raamsdonk, his fellow conference organizers, the It from Qubit collaboration, and UBC for their hospitality and their invitation to participate in Quantum Information in Quantum Gravity III, where this project partially took shape. A.B. acknowledges support from the Walter Burke Institute for Theoretical Physics and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. J.P. is supported partially by the Simons Foundation and partially by the Natural Sciences and Engineering Research Council of Canada. The IQIM is an NSF Physics Frontiers Center (NSF Grant PHY-1125565) that receives support from the Gordon and Betty Moore Foundation (GBMF-2644). The KITP is supported by the NSF under Grant No. NSF PHY-1125915. Author Contributions: All authors contributed to this paper equally. The authors declare no competing interests.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Barbara Groce Graduate Fellowship, CaltechUNSPECIFIED
Kavli Institute for Theoretical PhysicsUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-2644
Subject Keywords:Phase transitions and critical phenomena; Quantum information
Record Number:CaltechAUTHORS:20180614-124115479
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87116
Deposited By: Joy Painter
Deposited On:14 Jun 2018 20:39
Last Modified:12 Aug 2019 17:38

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