Information scrambling vs. decoherence -- two competing sinks for entropy

TL;DR

This paper investigates the interplay between quantum information scrambling and decoherence in open quantum systems, developing a thermodynamic framework and analyzing specific models to understand their competing effects on entropy.

Contribution

It introduces a thermodynamic description separating entropy production from scrambling and decoherence, with derived second law statements and numerical analysis of various models.

Findings

Entropy production can be decomposed into scrambling and decoherence contributions.

Decoherence can hinder the effectiveness of information scrambling in quantum systems.

Numerical models show the interplay affects entropy dynamics significantly.

Abstract

A possible solution of the information paradox can be sought in quantum information scrambling. In this paradigm, it is postulated that all information entering a black hole is rapidly and chaotically distributed across the event horizon making it impossible to reconstruct the information by means of any local measurement. However, in this scenario the effects of decoherence are typically ignored, which may render information scrambling moot in cosmological settings. In this work, we develop key steps towards a thermodynamic description of information scrambling in open quantum systems. In particular, we separate the entropy production into contributions arising from scrambling and decoherence, for which we derive statements of the second law. This is complemented with a numerical study of the Sachdev-Ye-Kitaev, Maldacena-Qi, XXX, mixed field Ising, Lipkin-Meshkov-Glick models in the presence of decoherence in energy or computational basis.