One-body entanglement as a quantum resource in fermionic systems
We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. We first provide a bipartitelike formulation of one-body entanglement, based on a Schmidt-like decomposition of a pure $N$-fermion state, from which the SPDM [together with the $(N-1)$-body density matrix] can be derived. It is then proved that under FLO operations, the initial and postmeasurement SPDMs always satisfy a majorization relation, which ensures that these operations cannot increase, on average, the one-body entanglement. It is finally shown that this resource is consistent with a model of fermionic quantum computation which requires correlations beyond antisymmetrization. More general free measurements and the relation with mode entanglement are also discussed.