Chaos in quantum channels
Name
JHEP02(2016)004_pdfa.pdf
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1.35 MB
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Author(s)
Hosur, Pavan
Qi, Xiao-Liang
Yoshida, Beni
Roberts, Daniel Adam
Date Issued
February 2016
Journal
Journal of High Energy Physics
Publisher
Springer/SISSA
Citation
Hosur, Pavan, Xiao-Liang Qi, Daniel A. Roberts, and Beni Yoshida. “Chaos in Quantum Channels.” J. High Energ. Phys. 2016, no. 2 (February 2016).
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP02(2016)004
