  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.
