Chaos in quantum channels

TL;DR

This paper investigates chaos and information scrambling in quantum channels by analyzing entanglement, out-of-time-order correlators, and tripartite information, linking chaos to information delocalization and providing diagnostic tools.

Contribution

It introduces the negativity of tripartite information as a new diagnostic for quantum scrambling and connects chaos diagnostics with entanglement properties of channels.

Findings

Decay of out-of-time-order correlators indicates near-vanishing mutual information.

Negativity of tripartite information measures information delocalization.

Numerical and analytic results support the link between chaos and information scrambling.

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.