Information Scrambling and Chaos in Open Quantum Systems

TL;DR

This paper extends the concept of out-of-time-ordered correlators to open quantum systems, providing an exact analytical framework that reveals how environmental decoherence affects information scrambling and chaos.

Contribution

It introduces an analytical formulation of bipartite OTOCs for open quantum systems, linking them to quantum channel distances and analyzing the effects of decoherence.

Findings

Open bipartite OTOC can be exactly expressed as a distance between quantum channels.

Environmental decoherence can obscure information scrambling signals.

Numerical studies differentiate between integrable and chaotic regimes in dissipative spin chains.

Abstract

Out-of-time-ordered correlators (OTOCs) have been extensively used over the last few years to study information scrambling and quantum chaos in many-body systems. In this paper, we extend the formalism of the averaged bipartite OTOC of Styliaris et al [Phys. Rev. Lett. 126, 030601 (2021)] to the case of open quantum systems. The dynamics is no longer unitary but it is described by more general quantum channels (trace preserving, completely positive maps). This "open bipartite OTOC" can be treated in an exact analytical fashion and is shown to amount to a distance between two quantum channels. Moreover, our analytical form unveils competing entropic contributions from information scrambling and environmental decoherence such that the latter can obfuscate the former. To elucidate this subtle interplay we analytically study special classes of quantum channels, namely, dephasing channels, entanglement-breaking channels, and others. Finally, as a physical application we numerically study dissipative many-body spin-chains and show how the competing entropic effects can be used to differentiate between integrable and chaotic regimes.