Physics behind the minimum of relative entropy measures for correlations

TL;DR

This paper explores the concept of nonfreeness, a measure of correlations based on relative entropy, showing it is minimized when the uncorrelated reference state shares the same one-particle density matrix as the correlated state, and discusses its implications.

Contribution

It demonstrates that the minimal relative entropy measure of correlations, called nonfreeness, is uniquely achieved with a reference state matching the one-particle density matrix, clarifying its physical relevance.

Findings

Nonfreeness is minimized when the uncorrelated state has the same one-particle density matrix.

Other uncorrelated states tend to overestimate correlations in physical scenarios.

The measure is applicable at finite temperatures and in correlation-enhanced orbital splitting.

Abstract

The relative entropy of a correlated state and an uncorrelated reference state is a reasonable measure for the degree of correlations. A key question is however which uncorrelated state to compare to. The relative entropy becomes minimal for the uncorrelated reference state that has the same one-particle density matrix as the correlated state. Hence, this particular measure, coined nonfreeness, is unique and reasonable. We demonstrate that for relevant physical situations, such as finite temperatures or a correlation enhanced orbital splitting, other choices of the uncorrelated state, even educated guesses, overestimate correlations.