One-body information loss in fermion systems

Abstract

We propose an entropic measure of nonclassical 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 nonentangled mixed states may nonetheless exhibit a nonzero information loss.