On separable states for composite systems of distinguishable fermions

We study separable (i.e., classically correlated) states for composite systems of spinless fermions that are distinguishable. For a proper formulation of entanglement formation for such systems, the state decompositions for mixed states should respect the univalence superselection rule. Fermion hopping always induces non-separability, while states with bosonic hopping correlation may or may not be separable. Under the Jordan-Klein-Wigner transformation from a given bipartite fermion system into a tensor product one, any separable state for the former is also separable for the latter. There are, however, U(1)-gauge invariant states that are non-separable for the former but separable for the latter.