One-body entanglement as a quantum resource in fermionic systems
| Autor: | Gigena, N., Di Tullio, M., Rossignoli, R. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 102, 042410 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.102.042410 |
| Popis: | 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. Comment: 11 pages, 1 figure |
| Databáze: | arXiv |
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