Nonfreeness and related functionals for measuring correlation in many-fermion states

TL;DR

This paper reviews the concept of nonfreeness and related correlation measures in many-fermion systems, highlighting their properties and significance in quantifying quantum correlations.

Contribution

It clarifies the definition of nonfreeness as a correlation measure and discusses its relationship with other entropy-based functionals in many-fermion states.

Findings

Nonfreeness equals the minimal entropy relative to free states.

Correlation functionals share additivity and monotonicity properties.

Nonfreeness has unique attractive properties among correlation measures.

Abstract

This article is a brief review of "nonfreeness" and related measures of "correlation" for many-fermion systems. The many-fermion states we deem "uncorrelated" are the gauge-invariant quasi-free states. Uncorrelated states of systems of finitely many fermions we call simply "free" states. Slater determinant states are free; all other free states are "substates" of Slater determinant states or limits of such. The nonfreeness of a many-fermion state equals the minimum of its entropy relative to all free states. Correlation functionals closely related to nonfreeness can be defined in terms of R\'enyi entropies; nonfreeness is the one that uses Shannon entropy. These correlation functionals all share desirable additivity and monotonicity properties, but nonfreeness has some additional attractive properties.