One-body information loss in fermion systems

We propose an entropic measure of non-classical correlations in general mixed states of fermion systems, based on the loss of information due to the unread measurement of the occupancy of single particle states of a given basis. When minimized over all possible single particle bases, the measure reduces to an entanglement entropy for pure states and vanishes only for states which are diagonal in a Slater determinant basis. The approach is also suitable for states having definite number parity yet not necessarily a fixed particle number, in which case the minimization can be extended to all bases related through a Bogoliubov transformation if quasiparticle mode measurements are also considered. General stationary conditions for determining the optimizing basis are derived. For a mixture of a general pure state with the maximally mixed state, a general analytic evaluation of the present measure and optimizing basis is provided, which shows that non-entangled mixed states may nonetheless exhibit a non-zero information loss.