Chaos in quantum channels

• Main Authors: Hosur, Pavan (Author), Qi, Xiao-Liang (Author), Yoshida, Beni (Author), Roberts, Daniel Adam (Contributor)
• Other Authors: Massachusetts Institute of Technology. Center for Theoretical Physics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: Springer/SISSA, 2016-03-04T19:16:02Z.
• Subjects: Article
• Online Access: Get fulltext

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.
Hertz Foundation
United States. Dept. of Energy (Cooperative Research Agreement Contract DE-SC0012567)