发表机构
Université Bourgogne Europe, CNRS, IMB UMR 5584; CNRS, ENS de Lyon, LPENSL, UMR5672（勃艮第欧洲大学; 法国国家科学研究中心，里昂高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将二体纠缠扩散推广至多体情形，定义了多体纠缠扩散，证明超图张量（HT）态是其最小化者，并刻画了谱超图张量（SHT）态的相关性质。
AI 中文摘要
二体纯态的纠缠结构由其纠缠谱表征，等价于整数k对应的Rényi-k纠缠熵族。取两个此类熵的差值定义了一种称为纠缠扩散的量，该量在局域操作下单调，且当且仅当态的纠缠谱为平坦时消失。我们引入该概念的多体推广，对于固定的D≥3个参与者，得到由满足一定条件的D边着色图对索引的映射族。该族中每个成员均为两个多体Rényi纠缠熵的差值，每个熵与一个局域幺正多项式不变量（在此语境下称为迹不变量）相关联，且被证明在局域操作下单调。随后我们指出，先前引入的所谓超图张量（HT）态族可被理解为平坦二体态族的多体对应。事实上，我们首先证明，当D=3时，三体纯态为HT态当且仅当它最小化某一特定（无穷）纠缠扩散族。其次，我们将HT态集嵌入更大的谱超图张量（SHT）态族中，该族由我们引入的新Ansatz定义。接着我们证明，对于任意D≥3，HT态可被唯一表征为SHT态中某一固定纠缠扩散的最小化者。我们还独立研究了SHT态：特别地，我们刻画了其在局域幺正变换下的轨道。最后，在此过程中，我们计算了局域维度为N的Haar随机态中若干纠缠扩散的渐近大-N期望值。
英文摘要
The entanglement structure of a bipartite pure state is characterized by its entanglement spectrum, or equivalently, by the family of Rényi-$k$ entanglement entropies with integer $k$. Taking the difference of two such entropies defines a quantity known as an entanglement spread, that is monotonous under local operations, and that vanishes if and only if the entanglement spectrum of the state is flat. We introduce a multipartite generalization of this notion which, for a fixed number $D\geq 3$ of parties, results in a collection of maps indexed by pairs of $D$-edge-colored graphs (obeying some condition). Each member of this collection takes the form of a difference of two multipartite Rényi entanglement entropies, each associated to a local unitary polynomial invariant (known in this context as a trace-invariant), and is shown to be monotonous under local operations. We then argue that a previously introduced family of so-called hypergraph-tensor (HT) states can be understood as a multipartite counterpart to the family of flat bipartite states. Indeed, we first prove that, when $D=3$, a tripartite pure state is HT if and only if it minimizes a particular (infinite) family of entanglement spreads. Second, we embed the set of HT states into the much larger family of spectral hypergraph-tensor (SHT) states, defined by a new Ansatz we introduce. We then prove that HT states can be uniquely characterized as the minimizers of some fixed entanglement spread among SHT states, for arbitrary $D\geq 3$. We also investigate SHT states in their own right: in particular, we characterize their orbits under local unitary transformations. Finally, along the way, the asymptotic large-$N$ expectation values of a number of entanglement spreads are computed in the Haar-random state of local dimension $N$.
Comments52 pages, 16 figures
