Signatures of quantum chaos in an out-of-time-order tensor

TL;DR

This paper introduces the out-of-time-order matrix (OTOM), a quantum analog of the OTOC, as an experimentally feasible method to measure quantum chaos and scrambling in various quantum systems.

Contribution

It proposes a fully quantum version of the out-of-time-order correlator, the OTOM, providing a new tool to identify quantum chaos through experimentally accessible measurements.

Findings

OTOM effectively detects chaos in random unitary processes.

OTOM successfully characterizes chaos in the quantum kicked rotor.

The method offers clear information-theoretic insights into quantum chaoticity.

Abstract

Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of interest interacts with a small quantum probe whose dynamical properties identify the chaoticity of the system. Specifically, we propose a fully quantum version of the out-of-time-order correlator (OTOC) - which we term the out-of-time-order matrix (OTOM) - whose correlations offer clear information theoretic meanings about the chaoticity of a process. We illustrate the utility of the OTOM as a signature of chaos using random unitary processes as well as in the quantum kicked rotor, where the chaoticity is tuneable.