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arXiv 2401.01014quant-ph
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多体场景下的纠缠层级

Entanglement hierarchies in multipartite scenarios

Hui Li, Ting Gao, Fengli Yan

备注：
10 pages, 3 figures
发表信息：
Chinese Journal of Physics 95 (2025) 337-347
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AI总结：

该研究针对多体量子态的纠缠层级表征问题，提出k-GM concurrence等系列层级化纠缠度量，建立其与已有度量的关系并推导下界，可更精细区分纠缠态且满足连续性等公理要求。

摘要：

本文研究了n体量子态的层级结构。我们提出了一整套层级化量化指标作为表征量子态的方法，这类指标超越了真正多体纠缠度量的范畴，能够精细识别不同的纠缠贡献。这类被称为k-GM concurrence（k体真正多体并发性）的量化指标，可从k非可分性的角度（k从n递减到2）将纠缠态明确划分为(n-1)个不同类别，且符合纠缠度量的公理条件。与k-ME concurrence（出自《物理评论A》2012年第86卷062323页）相比，我们提出的层级度量在区分同类纠缠态和度量连续性方面具备优势。此外，我们建立了k-ME concurrence与k-GM concurrence之间的关系，并进一步利用量子态的置换不变部分推导出k-GM concurrence的一个强下界。我们还对k-GM concurrence进行参数化，得到了两类更具普适性和完备性的量化指标：q-k-GM concurrence（q>1）和α-k-GM concurrence（0≤α<1），二者同样具备k-GM concurrence的所有性质。特别地，α-2-GM concurrence（0<α<1）判定GHZ态和W态属于同一层级，且被详细证明满足多量子比特系统中GHZ态比W态纠缠度更高的要求。

英文摘要：

In this paper, we investigate the hierarchical structure of the $n$-partite quantum states. We present a whole set of hierarchical quantifications as a method of characterizing quantum states, which go beyond genuine multipartite entanglement measures and allow for fine identification among distinct entanglement contributions. This kind of quantifications, termed $k$-GM concurrence, can unambiguously classify entangled states into $(n-1)$ distinct classes from the perspective of $k$-nonseparability with $k$ running from $n$ down to 2, and comply with the axiomatic conditions of an entanglement measure. Compared to $k$-ME concurrence [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.062323} {Phys. Rev. A \textbf{86}, 062323 (2012)}], the hierarchical measures proposed by us embody advantages in distinguishing same class entangled state and measuring continuity. In addition, we establish the relation between $k$-ME concurrence and $k$-GM concurrence, and further derive a strong lower bound on the $k$-GM concurrence by exploiting the permutationally invariant part of a quantum state. Furthermore, we parametrize $k$-GM concurrence to obtain two more general and complete categories of quantifications, $q$-$k$-GM concurrence $(q>1)$ and $α$-$k$-GM concurrence $(0\leqα<1)$, which obey the properties enjoyed by $k$-GM concurrence as well. In particular, $α$-$2$-GM concurrence $(0<α<1)$ determines that the GHZ state and the $W$ state belong to the same hierarchy, and it is proven in detail satisfying the requirement that the GHZ state is more entangled than the $W$ state in multiqubit systems.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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