Many-body localization and the emergence of quantum darwinism

TL;DR

This paper investigates how disorder in a quantum environment influences the emergence of quantum darwinism, revealing that high disorder enhances objectivity and may help preserve redundancy despite environmental interactions.

Contribution

It introduces the concept of lack of redundancy to quantify objectivity and links it to entanglement entropy, enabling estimation of the many-body mobility edge.

Findings

Disorder significantly promotes quantum darwinism.

A critical disorder level enhances environmental objectivity.

High disorder can mitigate redundancy loss due to intra-environment interactions.

Abstract

Quantum darwinism (QD) is the process responsible for the proliferation of redundant information in the environment of a quantum system that is being decohered. This enables independent observers to access separate environmental fragments and reach consensus about the system's state. In this work, we study the effect of disorder in the emergence of QD and find that a highly disordered environment is greatly beneficial for it. By introducing the notion of lack of redundancy to quantify objectivity, we show that it behaves analogously to the entanglement entropy (EE) of the environmental eigenstate taken as an initial state. This allows us to estimate the many-body mobility edge by means of our darwinistic measure, implicating the existence of a critical degree of disorder beyond which the degree of objectivity rises the larger the environment is. The latter hints the key role that disorder may play when the environment is of a thermodynamic size. At last, we show that a highly disordered evolution may reduce the spoiling of redundancy in the presence of intra-environment interactions.