Eur. Phys. J. D (2012) 66: 14
https://doi.org/10.1140/epjd/e2011-10654-x

Regular Article

Entropic entanglement criteria for Fermion systems

¹ Physics Department, University of Pretoria, Pretoria 0002, South Africa
² Instituto Carlos I de Física Teórica y Computacional and Departamento de Fisica Atomica, Molecular y Nuclear, University of Granada, Granada, Spain
³ National University La Plata, UNLP-CREG-IFILP-CONICET, C.C. 727, 1900 La Plata, Argentina
⁴ Departament de Física, Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca, Spain

^a e-mail: arplastino@ugr.es

Received: 16 November 2010
Received in final form: 8 April 2011
Published online: 25 January 2012

Abstract

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one-particle reduced density matrix, on the other hand. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi’s entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi’s entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.