Multipartite concurrence for identical-fermion systems

TL;DR

This paper introduces a multipartite concurrence measure for pure states of identical fermions, enabling detection of entanglement and expressing it as an observable, with applications to maximally entangled three-fermion states.

Contribution

It proposes a novel entanglement measure for indistinguishable fermions and shows how to compute it as an observable using two copies of the state.

Findings

Defined a multipartite concurrence for fermionic systems.

Optimized the measure for maximally entangled three-fermion states.

Expressed the concurrence as an observable with two state copies.

Abstract

We study the problem of detecting multipartite entanglement among indistinguishable fermionic particles. A multipartite concurrence for pure states of $N$ identical fermions, each one having a $d$-dimensional single-particle Hilbert space, is introduced. Such entanglement measure, in particular, is optimized for maximally entangled states of three identical fermions that play a role analogous to the usual (qubit) Greenberger-Horne-Zeilinger state. In addition, it is shown that the fermionic multipartite concurrence can be expressed as the mean value of an observable, provided two copies of the composite state are available.