Correlations, information backflow, and objectivity in a class of pure dephasing models

TL;DR

This paper investigates how correlations between a quantum system and its environment influence the emergence of classical objectivity, revealing that non-Markovian dynamics alone do not determine classicality but the nature of system-environment correlations does.

Contribution

It introduces a detailed analysis of the role of correlations in quantum Darwinism within dephasing models, showing that identical non-Markovian dynamics can differ in classical objectivity based on correlation profiles.

Findings

Correlations determine the emergence of classical objectivity.

Non-Markovianity does not necessarily hinder classical information proliferation.

Different microscopic models can produce the same reduced dynamics but differ in classicality.

Abstract

We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a class of dephasing models where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen-Shannon divergence and relative entropy, as well as changes in the environmental state, play in whether the conditions for classical objectivity within the quantum Darwinism paradigm are met. We demonstrate that for precisely the same non-Markovian reduced dynamics of the system arising from different microscopic models, some will exhibit quantum Darwinistic features, while others show no meaningful notion of classical objectivity is present. Furthermore, our results highlight that the non-Markovian nature of an environment does not a priori prevent a system from redundantly proliferating relevant information, but rather it is the system's ability to establish the requisite correlations that is the crucial factor in the manifestation of classical objectivity.