Chaos in quantum channels

A bstract 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 correla...

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Bibliographic Details
Published in:The journal of high energy physics 2016-02, Vol.2016 (2), p.1-49, Article 4
Main Authors: Hosur, Pavan, Qi, Xiao-Liang, Roberts, Daniel A., Yoshida, Beni
Format: Article
Language:English
Subjects:
AdS-CFT Correspondence
Channels
Chaos theory
Classical and Quantum Gravitation
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Correlators
Decomposition
Diagnostic systems
Elementary Particles
Evolution
Gauge-gravity correspondence
High energy physics
Holography and condensed matter physics (AdS/CMT)
Mathematical analysis
Mathematical models
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Random Systems
Regular Article - Theoretical Physics
Relativity Theory
String Theory
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP02(2016)004