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 R´enyi’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 R´enyi’s entropic
parameter is investigated. The extension of these criteria to systems of N identical fermions is also
considered.
