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Chaos in quantum channels

  • Pavan Hosur
  • Xiao-Liang Qi
  • Daniel A. RobertsEmail author
  • Beni Yoshida
Open Access
Regular Article - Theoretical Physics

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.

Keywords

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

Notes

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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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Pavan Hosur
    • 1
  • Xiao-Liang Qi
    • 1
  • Daniel A. Roberts
    • 2
    Email author
  • Beni Yoshida
    • 3
    • 4
  1. 1.Department of PhysicsStanford UniversityStanfordU.S.A.
  2. 2.Center for Theoretical Physics and Department of PhysicsMassachusetts Institute of TechnologyCambridgeU.S.A.
  3. 3.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  4. 4.Walter Burke Institute for Theoretical PhysicsCalifornia Institute of TechnologyPasadenaU.S.A.

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