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Chaos in quantum channels

  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 01 February 2016
  • volume 2016, Article number: 4 (2016)
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Chaos in quantum channels
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  • Pavan Hosur1,
  • Xiao-Liang Qi1,
  • Daniel A. Roberts2 &
  • …
  • Beni Yoshida3,4 

  • 4908 Accesses

  • 411 Citations

  • 15 Altmetric

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A preprint version of the article is available at arXiv.

Abstract

We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.

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Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. Department of Physics, Stanford University, 476 Lomita Mall, Stanford, California, 94305, U.S.A.

    Pavan Hosur & Xiao-Liang Qi

  2. Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, Massachusetts, 02139, U.S.A.

    Daniel A. Roberts

  3. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada

    Beni Yoshida

  4. Walter Burke Institute for Theoretical Physics, California Institute of Technology, 1200 E California Blvd, Pasadena, CA, 91125, U.S.A.

    Beni Yoshida

Authors
  1. Pavan Hosur
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  2. Xiao-Liang Qi
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Corresponding author

Correspondence to Daniel A. Roberts.

Additional information

ArXiv ePrint: 1511.04021

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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.

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Cite this article

Hosur, P., Qi, XL., Roberts, D.A. et al. Chaos in quantum channels. J. High Energ. Phys. 2016, 4 (2016). https://doi.org/10.1007/JHEP02(2016)004

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  • Received: 23 November 2015

  • Accepted: 18 January 2016

  • Published: 01 February 2016

  • DOI: https://doi.org/10.1007/JHEP02(2016)004

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Keywords

  • AdS-CFT Correspondence
  • Holography and condensed matter physics (AdS/CMT)
  • Gauge-gravity correspondence
  • Random Systems

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