Classifying two-body Hamiltonians for Quantum Darwinism

TL;DR

This paper identifies specific Hamiltonian properties necessary for quantum Darwinism to emerge, analyzing various models to establish conditions for classicality to arise from quantum systems.

Contribution

It introduces a set of commutation relations that Hamiltonians must satisfy for quantum Darwinism to occur in finite-dimensional systems.

Findings

Hamiltonians support quantum Darwinism if operators satisfy specific commutation relations.

Analysis of diverse models confirms the theoretical conditions for classicality emergence.

Provides a framework for classifying two-body Hamiltonians conducive to quantum Darwinism.

Abstract

Quantum Darwinism is a paradigm to understand how classically objective reality emerges from within a fundamentally quantum universe. Despite the growing attention that this field of research as been enjoying, it is currently not known what specific properties a given Hamiltonian describing a generic quantum system must have to allow the emergence of classicality. Therefore, in the present work, we consider a broadly applicable generic model of an arbitrary finite-dimensional system interacting with an environment formed from an arbitrary collection of finite-dimensional degrees of freedom via an unspecified, potentially time-dependent Hamiltonian containing at most two-body interaction terms. We show that such models support quantum Darwinism if the set of operators acting on the system which enter the Hamiltonian satisfy a set of commutation relations with a pointer observable and with one other. We demonstrate our results by analyzing a wide range of example systems: a qutrit interacting with a qubit environment, a qubit-qubit model with interactions alternating in time, and a series of collision models including a minimal model of a quantum Maxwell demon.