Entropic Entanglement Criteria for Fermion Systems

TL;DR

This paper develops entanglement detection criteria for systems of identical fermions using entropy inequalities, extending to N-fermion systems and analyzing the effectiveness of Renyi's entropy in identifying entanglement.

Contribution

It introduces novel entanglement criteria based on entropy inequalities for fermion systems, including mixed states and N-fermion extensions, with analysis of Renyi's entropy parameter effects.

Findings

Criteria successfully detect entanglement in various fermionic states

Detection efficiency varies with Renyi's entropy parameter

Extended criteria applicable to N-fermion systems

Abstract

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one particle reduced density matrix, on the other one. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on R\'enyi's entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on R\'enyi's entropic parameter is investigated. The extension of these criteria to systems of $N$ identical fermions is also considered.