Relation between the Dynamics of the Reduced Purity and Correlations

TL;DR

This paper explores how changes in a quantum system's reduced purity over time indicate the presence of correlations with its environment, highlighting the fundamental link between local dynamics and correlations.

Contribution

It establishes a general relation showing that a non-zero rate of change in reduced purity implies non-zero correlations for systems with unbounded Hamiltonians and finite variance.

Findings

Non-zero purity change indicates correlations with environment.

The relation holds for unbounded Hamiltonians with finite variance.

Local dynamical information reflects correlation dynamics.

Abstract

A general property of the relation between the dynamics of the reduced purity and correlations is investigated in quantum mechanical systems. We show that a non-zero time-derivative of the reduced purity of a system implies the existence of non-zero correlations with its environment under any unbounded Hamiltonians with finite variance. This shows the role of local dynamical information on the correlations, as well as the role of correlations in the mechanism of purity change.