Chaos in quantum channels

Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni

doi:10.1007/JHEP02(2016)004

Chaos in quantum channels

Pavan Hosur
(
- Stanford U., Phys. Dept.
)
,
Xiao-Liang Qi
(
- Stanford U., Phys. Dept.
)
,
Daniel A. Roberts
(
- MIT, Cambridge, Dept. Phys. and
- MIT, Cambridge, CTP
)
,
Beni Yoshida
(
- Perimeter Inst. Theor. Phys. and
- Caltech
)

Nov 12, 2015

49 pages

Published in:

JHEP 02 (2016) 004

Published: Feb 1, 2016

e-Print:

1511.04021 [hep-th]

DOI:

10.1007/JHEP02(2016)004

Report number:

MIT-CTP-4733

View in:

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Abstract: (arXiv)

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.

Note:

44+17 pages, many figures. v2: typos fixed, references added, statements clarified. v3: minor confusion alleviated

AdS-CFT Correspondence
Holography and condensed matter physics (AdS/CMT)
Gauge-gravity correspondence
Random Systems
chaos
correlation function
delocalization
entanglement
unitarity
network

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