  We characterize and classify quantum correlations in two-fermion systems
having 2K single-particle states. For pure states we introduce the Slater
decomposition and rank (in analogy to Schmidt decomposition and rank), i.e. we
decompose the state into a combination of elementary Slater determinants formed
by mutually orthogonal single-particle states. Mixed states can be
characterized by their Slater number which is the minimal Slater rank required
to generate them. For K=2 we give a necessary and sufficient condition for a
state to have a Slater number of 1. We introduce a correlation measure for
mixed states which can be evaluated analytically for K=2. For higher K, we
provide a method of constructing and optimizing Slater number witnesses, i.e.
operators that detect Slater number for some states.
