Quantum Darwinism in a composite system: Objectivity versus classicality

TL;DR

This paper explores how quantum Darwinism manifests in a two-qubit system interacting with an environment, revealing a split between classical objectivity and non-classical quantum signatures within composite systems.

Contribution

It provides an analytical study of quantum Darwinism in a composite system with decoherence-free subspaces, highlighting the coexistence of classical and quantum information proliferation.

Findings

Part of the system's information is redundantly stored in the environment.

Quantum discord indicates non-classical correlations between system and environment.

Information accessible from the environment appears classical due to discord asymmetry.

Abstract

We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an $N$-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems.