Quantum Darwinism in a structured spin environment

TL;DR

This paper investigates how quantum Darwinism signatures emerge or are suppressed in a structured spin environment, revealing the influence of environment structure, initial states, and interactions on classical objectivity.

Contribution

It introduces an extended 'onion' spin model to analyze the conditions affecting quantum Darwinism, highlighting the role of environment layers and initial states in the emergence of classicality.

Findings

Redundancy plateaux appear transiently when environment chains are considered as indivisible fragments.

Layer-specific quantum Darwinism is highly sensitive to interaction details.

Magnetic field strength influences the presence of quantum Darwinistic features in ground state initializations.

Abstract

We examine the emergence and suppression of signatures of quantum Darwinism when the system of interest interacts with a complex, structured environment. We introduce an extended spin-star model where the system is coupled to $N$ independent spin-chains. Each site of the chain then lives in a definite layer of the environment, and hence we term this the "onion" model. We fix the system-environment interaction such that classical objectivity is guaranteed if the environment consists of a single layer. Considering a fully factorized initial state for all constituent sub-systems, we then examine how the emergence and proliferation of signatures of quantum Darwinism are delicately dependent on the chain interaction, establishing that when the chains are considered as indivisible fragments to be interrogated, characteristic redundancy plateaux are always observed at least transiently. In contrast, observing a redundant encoding in a specific layer is highly sensitive to the nature of the interaction. Finally, we consider the case in which each chain is initialized in the ground state of the interaction Hamiltonian, establishing that this case shares the qualitative features of the factorized initial state case, however now the strength of the applied magnetic field has a significant impact on whether quantum Darwinism can be observed. We demonstrate that the presence or absence of quantum Darwinistic features can be understood by analysing the correlations within a layer using total mutual information and global quantum discord.