Chaos in quantum channels
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.
Additional Information
© 2016 The Authors. 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. Article funded by SCOAP3. Received: November 23, 2015; Accepted: January 18, 2016; Published: February 1, 2016. This work began at KITP, and the authors would like to acknowledge the KITP programs "Entanglement in Strongly-Correlated Quantum Matter" and "Quantum Gravity Foundations: UV to IR." We would also like to thank Tarun Grover, Aram Harrow, Patrick Hayden, Matt Headrick, Isaac Kim, John Preskill, Steve Shenker and Douglas Stanford for discussions, and Douglas Stanford for comments on the draft. PH and XLQ are supported by the David and Lucile Packard foundation. XLQ is also partially supported by the Templeton foundation. DR is supported by the Fannie and John Hertz Foundation and is also very thankful for the hospitality of the Stanford Institute for Theoretical Physics during a stage or two of this work. DR also acknowledges the U.S. Department of Energy under cooperative research agreement Contract Number DE-SC0012567. This paper was brought to you by the butterfly effect. BY is supported by the David and Ellen Lee Postdoctoral fellowship and the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.Attached Files
Published - art_10.1007_JHEP02_2016_004.pdf
Submitted - 1511.04021v2.pdf
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Additional details
- Eprint ID
- 64779
- Resolver ID
- CaltechAUTHORS:20160225-153036827
- David and Lucile Packard Foundation
- John Templeton Foundation
- Fannie and John Hertz Foundation
- DE-SC0012567
- Department of Energy (DOE)
- David and Ellen Lee Postdoctoral Fellowship
- Government of Canada
- Province of Ontario Ministry of Research and Innovation
- SCOAP3
- Created
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2016-02-26Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics