Commutativity and the emergence of classical objectivity

TL;DR

This paper investigates how multiple environments interacting with a quantum system influence the emergence of classical objectivity, highlighting the importance of commutativity in system-environment interactions for information redundancy.

Contribution

It analyzes the effects of coupled baths with commuting and non-commuting interactions on the formation of classical objectivity in quantum systems.

Findings

Commuting interactions preserve information redundancy.

Non-commuting, thermalising interactions degrade correlations.

Long-term loss of classical objectivity conditions due to non-commuting effects.

Abstract

We examine how the ability of a system to redundantly proliferate relevant information about its pointer states is affected when it is coupled to multiple baths. To this end, we consider a system in contact with two baths: one -- termed the {\it accessible} environment -- which, on its own, induces a pure dephasing mechanism on the state of the system and satisfies the conditions for classical objectivity to be established. The second environment, which we dub as {\it inaccessible}, affects the system in two physically relevant ways. Firstly, we consider an interaction that commutes with the Hamiltonian describing the interaction between system and accessible bath. It thus also gives rise to dephasing of the system, albeit on different time scales. Secondly, we consider a thermalising interaction, which does not commute with the system-accessible environment Hamiltonian. While the former still allows the system to redundantly encode its state into the accessible environment, the latter degrades the correlations, eventually destroying them in the long-time limit, and thus leads to a loss of the conditions necessary for classical objectivity to be established. This sheds light on the role that commutativity between the various system-bath interaction terms plays when establishing the conditions for classical objectivity to be supported.