Fermionic Genuine Multiparty Entanglement

Abstract

Entanglement can show fundamentally different behavior in fermionic systems. However, while bipartite measures of fermionic entanglement have been established, genuine multiparty entanglement (GME) in fermionic systems is much less understood. We introduce an efficiently computable measure (via semi-definite programming) of fermionic GME, fermion genuine multiparty negativity (fGMN), and show that it is an entanglement monotone and a natural multipartite extension of the fermionic negativity. Using this measure, we find many states which have fGMN but no non-fermionic GME, including large classes of fermionic stabilizer states. The fGMN also displays some major phenomenological differences to the bipartite fermionic negativity, such as finite sudden death points over separation and temperature.