A measure of tripartite entanglement in bosonic and fermionic systems

TL;DR

This paper introduces an efficient criterion for measuring tripartite entanglement in mixed states of identical particles, accounting for quantum statistics and avoiding superselection rule violations.

Contribution

It develops a generalized tripartite negativity measure applicable to bosonic and fermionic systems, enhancing entanglement quantification methods for identical particles.

Findings

Bosonic bunching leads to lower quantum correlations.

Fermionic statistics result in higher entanglement values.

Entanglement dynamics depend on particle quantum statistics.

Abstract

We describe an efficient theoretical criterion suitable for the evaluation of the tripartite entanglement of any mixed three-boson or -fermion state, based on the notion of the entanglement of particles for bipartite systems of identical particles. Our approach allows one to quantify the accessible amount of quantum correlations in the systems without any violation of the local particle number superselection rule. A generalization of the tripartite negativity is here applied to some correlated systems including the continuous-time quantum walks of identical particles (both for bosons and fermions) and compared with other criteria recently proposed in the literature. Our results show the dependence of the entanglement dynamics upon the quantum statistics: the bosonic bunching results into a low amount of quantum correlations while Fermi-Dirac statistics allows for higher values of the entanglement.