论文标题
费米昂系统中的多体纠缠
Many-body entanglement in fermion systems
论文作者
论文摘要
我们基于$ m <n $和$（n-m）$ fermions的状态，介绍了一个普通的二分般的表示和施密特的分解。它与减少的$ M $ - 和$（N-M）$ - 体密度矩阵（DMS）的连接，这些矩阵在此类状态下具有相同的频谱。在这种情况下，$ m $ - 体纠缠的概念自然而然地出现，从而概括了一体纠缠的概念。然后得出了正常化的$ m $ body DM满足的严格多数化关系，这意味着，在具有这些DMS作为测量后状态的一类操作下，相关的熵平均不会增加。此外，这种熵是由一系列操作产生的平均两分纠缠熵的上限，这些操作将原始状态映射到$ m $ $ $ $和$ n-m $有效区分的双方状态。还提供了一些密切相关的费米子状态中$ m $ dms的频谱的分析评估。
We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and $(N-M)$-body density matrices (DMs), which have the same spectrum in such states. The concept of $M$-body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement. Rigorous majorization relations satisfied by the normalized $M$-body DM are then derived, which imply that the associated entropy will not increase, on average, under a class of operations which have these DMs as post-measurement states. Moreover, such entropy is an upper bound to the average bipartite entanglement entropy generated by a class of operations which map the original state to a bipartite state of $M$ and $N-M$ effectively distinguishable fermions. Analytic evaluation of the spectrum of $M$-body DMs in some strongly correlated fermionic states is also provided.
