Quantum Darwinism in a Composite System: Objectivity versus Classicality.

Barış Çakmak,Steve Campbell,Özgür E Müstecaplıoğlu,Mauro Paternostro,Bassano Vacchini

doi:10.3390/e23080995

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.

Highlights

The theory of open quantum systems provides frameworks to describe how an environment destroys quantum superpositions
We have examined the emergence of quantum Darwinism for a composite system consisting of two qubits interacting with a N-partite bath
For an excitation-preserving interaction between the system qubits, we established that the system information is faithfully, redundantly encoded throughout the environment; we see the emergence of clear Darwinistic signatures

Summary

Introduction

The theory of open quantum systems provides frameworks to describe how an environment destroys quantum superpositions. Quantum Darwinism [1,2,3] and spectrum broadcast structures [4,5] establish mathematically rigorous approaches to quantitatively assess the mechanisms by which classically objective, accessible states emerge. The former employs an entropic approach, where classical objectivity follows from the redundant encoding of copies of the system’s pointer states (preferred basis states immune to spoiling by system–environment coupling) across fragments of the environment.

Composite System Model

Quantum Darwinism and Objectivity

Strong Quantum Darwinism

Conclusions