发表机构
School of Mathematics and Data Science, Jiangnan University; School of Mathematical Sciences, Beihang University; School of Mathematical Sciences, Capital Normal University（江南大学数学与数据科学学院; 北京航空航天大学数学科学学院; 首都师范大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究局部酉Bargmann不变量（LUBIs）能否充分判定多体态的局部酉（LU）等价性，证明对单方约化矩阵非简并的CLC态成立，并给出简并情形下反例。
AI 中文摘要
局部酉（LU）等价态对于理解量子纠缠的结构至关重要。我们基于LU Bargmann不变量（LUBIs）研究LU等价性。我们考虑对于哪些态，LUBIs足以确保LU等价性。我们关注一类具有完全局部交换性的多体态，称为CLC态。我们首先证明，对于多体CLC态，如果其单方约化密度矩阵是对角且非简并的，则所有LUBIs足以确保局部置换等价性。利用CLC性质在局部操作下保持不变的事实，我们验证了对于单方约化密度矩阵非简并的多体CLC态，LUBIs也足以确保其LU等价性。此外，当单方约化密度矩阵简并时，我们提出了两量子比特和三量子比特系统的具体例子，表明存在共享所有LUBIs但并非LU等价的态。
英文摘要
Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.
