Uncertainty relations and entanglement in fermion systems

Abstract

The violation of uncertainty relations is used as a signature of entanglement for both pure and mixed states of two identical fermions. In the case of fermions with a four-dimensional single-particle Hilbert space we obtain several different types of uncertainty-related entanglement criteria based on local uncertainty relations, on the sum of variances of projectors, and on various entropic measures. Within the latter approach we consider either entropic uncertainty relations involving a single observable or relations based upon the sum of entropies associated with more than one observable. We extend the projector-based entanglement criterion to the case of two-fermion and three-fermion systems with a six-dimensional single-particle Hilbert space.