Multipartite concurrence for identical fermions

A.P. MAJTEY; A. VALDÉS-HERNÁNDEZ; P.A. BOUVRIE; A.R. PLASTINO

Jornada; VII Conference on Quantum Foundations: 90 years of uncertainty; 2017

A fundamental feature of quantum systems composed of N identical fermions is that their elementary (antisymmetric) pure state is a single Slater determinant. Such property has led to the notion of fermionic entanglement, associated with the quantum correlations exhibited on top of the Slater correlations. This opens the problem of constructing (fermionic) entanglement measures, that properly quantify the extra correlations beyond those due to the indistinguishability of the parties. Here we generalize previously existing fermionic entanglement criteria, and introduce a multipartite fermionic concurrence valid for pure states of N identical fermions, each one having a d-dimensional single-particle Hilbert space. It is shown that the proposed concurrence can be expressed as the mean value of an observable, provided two copies for the composite state are available. In addition, we find that the introduced entanglement measure is optimized for maximally entangled states of three identical fermions that play a role analogous to the usual (qubit) GHZ state.