Correlation in states of two identical particles

TL;DR

This paper defines a new measure of quantum correlation in two-particle states based on residual information beyond the one-particle reduced density matrix, providing analytical formulas and comparing correlation degrees among particle types.

Contribution

It introduces a residual information-based correlation measure for identical particles and derives analytical results, enabling computation for any two-particle state.

Findings

Correlation decreases from bosons to fermions to distinguishable particles.

Analytical formulas make the correlation measure computationally feasible.

The measure captures residual information beyond the one-particle reduced density matrix.

Abstract

We identify the correlation in a state of two identical particles as the residual information beyond what is already contained in the 1-particle reduced density matrix, and propose a correlation measure based on the maximum entropy principle. We obtain the analytical results of the correlation measure, which make it computable for arbitrary two-particle states. We also show that the degrees of correlation in the same two-particle states with different particle types will decrease in the following order: bosons, fermions, and distinguishable particles.