What are the systems that decohere?

TL;DR

This paper argues that the problem of defining the system-environment boundary in decoherence is a pseudo-problem, as decoherence depends on the relevant observables, and demonstrates unexpected results in the spin-bath model.

Contribution

It clarifies that the system-environment cut in decoherence is relative to observables and presents new findings on decoherence with small environments in the spin-bath model.

Findings

Decoherence depends on relevant observables chosen by the measurement setup.

Unexpected decoherence occurs with very small environments in the spin-bath model.

The perceived problem of the system-environment cut is a pseudo-problem.

Abstract

The fact that the Environment Induced Decoherence approach offers no general criterion to decide where to place the "cut" between system and environment has been considered as a serious conceptual problem of the proposal. In this letter we argue that this is actually a pseudo-problem, which is dissolved by the fact that decoherence is a phenomenon relative to the relevant observables selected by the measuring arrangement. We also show that, when the spin-bath model is studied from this perspective, certain unexpected results are obtained, as that of a system decohering in interaction with a very small environment.