Application of quantum Darwinism to a structured environment

TL;DR

This paper investigates how quantum Darwinism explains the emergence of classicality in a qubit coupled to structured environments, revealing how information redundancy and non-Markovian effects influence classical and quantum correlations.

Contribution

It applies quantum Darwinism to a structured environment model, analyzing information redundancy and correlations, and links redundancy to non-Markovian dynamics as a new insight.

Findings

Significant information redundancy emerges during decoherence.

Classical information is non-redundant in both environment and pseudomode components.

Redundancy acts as a witness to non-Markovianity, correlating with information back-flow.

Abstract

Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic sub-environments. We examine the degree to which the same classical information is encoded across collections of: (i) complete sub-environments, and (ii) residual "pseudomode" components of each sub-environment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be non-redundant in both cases (i) and (ii). Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information back-flow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.