  We show that with respect to any bipartite division of modes, pure fermion
gaussian states display the same type of structure in its entanglement of modes
as that of the BCS wave function, namely, that of a tensor product of entangled
two-mode squeezed fermion states. We show that this structure applies to a
wider class of "isotropic" mixed fermion states, for which we derive necessary
and sufficient conditions for mode entanglement.
