Separability criteria and entanglement measures for pure states of N identical fermions

Abstract

The study of the entanglement properties of systems of N fermions has\nattracted considerable interest during the last few years. Various separability\ncriteria for pure states of N identical fermions have been recently discussed\nbut, excepting the case of two-fermions systems, these criteria are difficult\nto implement and of limited value from the practical point of view. Here we\nadvance simple necessary and sufficient separability criteria for pure states\nof N identical fermions. We found that to be identified as separable a state\nhas to comply with one single identity involving either the purity or the von\nNeumann entropy of the single-particle reduced density matrix. These criteria,\nbased on the verification of only one identity, are drastically simpler than\nthe criteria discussed in the recent literature. We also derive two\ninequalities verified respectively by the purity and the entropy of the single\nparticle, reduced density matrix, that lead to natural entanglement measures\nfor N-fermion pure states. Our present considerations are related to some\nclassical results from the Hartree-Fock theory, which are here discussed from a\ndifferent point of view in order to clarify some important points concerning\nthe separability of fermionic pure states.\n