发表机构
University of Siena; INFN Sezione di Perugia; Wilhelm-Johnen-Straße, 52428 Jülich, Germany; Department of Physics and Materials Science, University of Luxembourg（锡耶纳大学; 佩鲁伽国家核物理研究所分部; 威廉·约翰恩大街，德国于利希; 卢森堡大学物理与材料科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从几何角度研究量子纠缠，提出基于Fubini--Study度量的纠缠距离（ED），并证明其能再现双量子比特态的并发度和纠缠熵等标准度量，为纠缠提供几何解释。
AI 中文摘要
量子纠缠是量子信息理论中的一种基本资源，然而其一般性的刻画和量化仍然具有挑战性，尤其是在多体系统中。在本工作中，我们从几何角度研究纠缠，重点关注由多量子比特量子态的射影希尔伯特空间上的Fubini--Study度量所诱导的黎曼结构。通过利用该度量的局域幺正不变性，我们推导出纠缠距离（ED），这是一种几何度量，它将纠缠量化为局域操作所产生的Fubini--Study距离平方和局域最小化的一种阻碍。我们分析了纯多量子比特态的ED性质，并讨论了其在局域操作和经典通信下的行为。特别地，我们表明ED在明确且受限的设置中再现了既有的纠缠度量。对于两个量子比特的纯态，ED约化为并发度的一个精确单调函数，并且独立地约化为纠缠熵的一个显式单调函数。这些结果在当前框架内为标准双粒子纠缠度量提供了清晰的几何解释，同时突出了在双量子比特情形之外此类对应关系的局限性。
英文摘要
Quantum entanglement is a fundamental resource in quantum information theory, yet its general characterization and quantification remain challenging, especially in multipartite systems. In this work we investigate entanglement from a geometric perspective, focusing on the Riemannian structure induced by the Fubini--Study metric on the projective Hilbert space of multi-qubit quantum states. By exploiting the local-unitary invariance of this metric, we derive the entanglement distance (ED), a geometric measure that quantifies entanglement as an obstruction to locally minimizing the sum of squared Fubini--Study distances generated by local operations. We analyze the properties of ED for pure multi-qubit states and discuss its behavior under local operations and classical communication. In particular, we show that ED reproduces established entanglement measures in well-defined and restricted settings. For pure states of two qubits, ED reduces to an exact monotone function of the concurrence and, independently, to an explicit monotone function of the entropy of entanglement. These results provide a clear geometric interpretation of standard bipartite entanglement measures within the present framework, while highlighting the limitations of such correspondences beyond the two-qubit case.
Journal refEntropy 2026, 28, 299
