Out-of-time-ordered measurements as a probe of quantum dynamics

TL;DR

This paper introduces the out-of-time-ordered measurement (OTOM), a new experimental tool that captures quantum dynamics similarly to OTOCs but with simpler measurement requirements, enabling better exploration of quantum systems.

Contribution

The paper proposes OTOM as an accessible alternative to OTOCs for probing quantum dynamics, linking it theoretically to OTOCs and demonstrating its effectiveness through numerical simulations.

Findings

OTOM closely relates to OTOC in doubled systems

OTOM reveals quantum dynamics features hidden to classical measures

Numerical simulations confirm OTOM's effectiveness in various regimes

Abstract

Probing the out-of-equilibrium dynamics of quantum matter has gained renewed interest owing to immense experimental progress in artifcial quantum systems. Dynamical quantum measures such as the growth of entanglement entropy (EE) and out-of-time ordered correlators (OTOCs) have been shown, theoretically, to provide great insight by exposing subtle quantum features invisible to traditional measures such as mass transport. However, measuring them in experiments requires either identical copies of the system, an ancilla qubit coupled to the whole system, or many measurements on a single copy, thereby making scalability extremely complex and hence, severely limiting their potential. Here, we introduce an alternate quantity $-$ the out-of-time-ordered measurement (OTOM) $-$ which involves measuring a single observable on a single copy of the system, while retaining the distinctive features of the OTOCs. We show, theoretically, that OTOMs are closely related to OTOCs in a doubled system with the same quantum statistical properties as the original system. Using exact diagonalization, we numerically simulate classical mass transport, as well as quantum dynamics through computations of the OTOC, the OTOM, and the EE in quantum spin chain models in various interesting regimes (including chaotic and many-body localized systems). Our results demonstrate that an OTOM can successfully reveal subtle aspects of quantum dynamics hidden to classical measures, and crucially, provide experimental access to them.