One-body information loss in fermion systems

TL;DR

This paper introduces an entropic measure of non-classical correlations in fermion systems based on information loss from measurements, unifying entanglement and classicality detection in mixed states.

Contribution

It proposes a new entropic measure for fermion correlations that accounts for basis optimization and extends to states with definite number parity, including quasiparticle modes.

Findings

The measure reduces to entanglement entropy for pure states.

It vanishes for states diagonal in a Slater determinant basis.

Non-entangled mixed states can still show non-zero information loss.

Abstract

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.