One-body entanglement as a resource in fermion systems

GIGENA, NICOLÁS ALEJANDRO; DI TULLIO, MARCO; ROSSIGNOLI, RAÚL DANTE

Al Hoceima

Workshop; School and Workshop on Quantum Information and Thermodynamics at the Nanoscale; 2020

ICTP

We show that one-body entanglement, which quantifies the mixedness of the eigenvalues of the single particle density matrix (SPDM) of a fermionic system, can be considered as a quantum resource. We define the free states and operations for this resource through majorization, and show that pure state conversion via these operations will in general imply a decrease in one-body entanglement. It is then demonstrated that fermion linear optics operations, which include onebody unitary transformations and measurements of the occupancy of single particle modes, are free operations implying a majorization relation between the initial and postmeasurement SPDMs. Finally, it is shown that the ensuing resource is consistent with a model of fermionic quantum computation. A general bipartite-like formulation of one-body entanglement is also discussed.