Majorization-based entanglement criterion for fermion systems using the von Neumann entropy

Abstract

We use the Schur concavity of the von Neumann entropy and introduce a majorization-based entanglement criterion for the states of systems consisting of identical fermions. This criterion is in the form of an inequality between the von Neumann entropies of the total density matrix and the single-particle reduced density matrix which have to be satisfied by the separable states of such systems, and therefore, its violation indicates the entanglement. Our criterion is an improved version of the one introduced by Zander et al. (in Eur. Phys. J. D 66: 14, 2012). To illustrate its utility, we use the criterion to various illustrative instances of the families of mixed states and find that when the single-particle Hilbert spaces are of dimension four, the criterion indicates all the entangled states within the families under consideration.