Generalized Loschmidt echo and information scrambling in open systems

TL;DR

This paper extends the concepts of Loschmidt echo and OTOC to open quantum systems with dissipation, revealing universal behaviors and spectral features, and proposes experimental measurement protocols for information scrambling in such systems.

Contribution

It introduces a generalized framework for LE and OTOC in open systems, analyzes their universal dynamics, and connects them to entropy measures, advancing understanding of quantum information scrambling under dissipation.

Findings

Universal structure of LE in weak dissipation

Two-minima spectral structure in strong dissipation

Proposed experimental measurement protocol for OTOC

Abstract

Quantum information scrambling, typically explored in closed quantum systems, describes the spread of initially localized information throughout a system and can be quantified by measures such as the Loschmidt echo (LE) and out-of-time-order correlator (OTOC). In this paper, we explore information scrambling in the presence of dissipation by generalizing the concepts of LE and OTOC to open quantum systems governed by Lindblad dynamics. We investigate the universal dynamics of the generalized LE across regimes of weak and strong dissipation. In the weak dissipation regime, we identify a universal structure, while in the strong dissipation regime, we observe a distinctive two-local-minima structure, which we interpret through an analysis of the Lindblad spectrum. Furthermore, we establish connections between the thermal averages of LE and OTOC and prove a general relation between OTOC and R\'enyi entropy in open systems. Finally, we propose an experimental protocol for measuring OTOC in open systems. These findings provide deeper insights into information scrambling under dissipation and pave the way for experimental studies in open quantum systems.