Volume 86, Number 2, April 2009
Article Number 20005
Number of page(s) 5
Section General
Published online 05 May 2009
EPL, 86 (2009) 20005
DOI: 10.1209/0295-5075/86/20005

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

A. R. Plastino1, 2, D. Manzano1, 3 and J. S. Dehesa1, 3

1   Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada - 18071-Granada, Spain, EU
2   National University La Plata, UNLP-CREG-Conicet - C.C. 727, 1900 La Plata, Argentina
3   Departamento de Física Atómica, Molecular, y Nuclear, Universidad de Granada - 18071-Granada, Spain, EU

received 26 January 2009; accepted in final form 24 March 2009; published April 2009
published online 5 May 2009

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

03.65.Ta - Foundations of quantum mechanics; measurement theory.
03.65.Ud - Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.).

© EPLA 2009