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 bipartite-like 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 DM) can be derived. It is then shown that under FLO operations, the initial and post-measurement 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 relation with mode entanglement are also d iscussed.

中文翻译：

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单体纠缠作为费米子系统中的量子资源

我们表明，单体缠结是一种纯费米子态与Slater行列式（SD）的偏差的量度，由单粒子密度矩阵（SPDM）的混合度确定，可以视为一种量子资源。相关的理论将SD及其凸包作为自由状态，并将数量守恒的费米子线性光学操作（FLO）作为基本的自由操作，其中包括单体unit变换和单个粒子模式占有率的测量。我们首先基于纯的Schmidt分解，提供一个类似二分体的一体式缠结公式$ñ$-fermion状态，SPDM从该状态（与 $（ñ-\mathrm{1个}）$-body DM）。然后表明，在FLO操作下，初始和测量后的SPDM始终满足主要化关系，这确保了这些操作平均不会增加单身纠缠。最终表明，该资源与费米子量子计算模型一致，该模型需要反对称以外的相关性。还讨论了更一般的自由测量以及与模态纠缠的关系。