Decoherence as a high-dimensional geometrical phenomenon

TL;DR

This paper introduces a geometric formalism to analyze decoherence as a high-dimensional phenomenon, providing quantitative estimates of decoherence levels based on reservoir sizes and exploring links with entanglement entropy.

Contribution

It develops a general mathematical framework to study decoherence geometrically, connecting system-reservoir dimensions with decoherence and entanglement entropy.

Findings

Decoherence can be characterized as a high-dimensional geometric effect.

Quantitative estimates relate reservoir sizes to decoherence levels.

Links between decoherence and entanglement entropy are established.

Abstract

We develop a mathematical formalism that allows to study decoherence with a great level generality, so as to make it appear as a geometrical phenomenon between reservoirs of dimensions. It enables us to give quantitative estimates of the level of decoherence induced by a purely random environment on a system according to their respectives sizes, and to exhibit some links with entanglement entropy.