Resumen:
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.
Resumen:
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 Nfermion
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.
