Spectral properties of bipartite fermionic systems

Since Hilbert space of fermionic states does not have tensor product structure, pure bipartite fermionic systems are not subject to conventional Schmidt decomposition. As a result, spectra of two subsystems may differ. In general case, the Araki-Lieb relation can be violated. We find necessary and sufficient conditions for the coincidence of subsystems' spectra of pure fermionic state with variable number of particles. Equispectral states are reduced by local unitaries to the states satisfying parity superselection rule.