AI 中文总结
该研究解决了不等局域维数 bipartite 和 tripartite 系统中具有最小非定域性的正交量子态集合的构造问题，给出了通用构造方法并完成了具体系统的构造。
AI 中文摘要
最小非定域性研究旨在确定非定域量子态集合的最小基数，但不等局域维数的 bipartite 或 tripartite 量子系统中非定域态集合的构造问题仍未解决。本文首先给出 $\boldsymbol{\rm C}^4 \boldsymbol{\rm \times C}^7$ 量子系统中具有最小非定域性的正交量子态集合的构造方法，随后提出不等局域维数 bipartite 量子系统中同类集合的通用构造方法，进一步将该方法推广至不等局域维数 tripartite 量子系统，对满足 $5 \boldsymbol{\rm \times} d_1 < d_2 < d_3$ 的 $\boldsymbol{\rm C}^{d_1} \boldsymbol{\rm \times C}^{d_2} \boldsymbol{\rm \times C}^{d_3}$ 量子系统构造出具有最小非定域性的正交量子态集合。本工作解决了不等局域维数 bipartite 和 tripartite 系统中具有最小非定域性的正交态集合的构造问题。
英文摘要
The research on minimal nonlocality aims to determine the minimal cardinality of nonlocal sets of quantum states. However, the construction of a nonlocal set of states in bipartite or tripartite quantum systems with unequal local dimensions remains unsolved. In this paper, we first give a method to construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb{C}^{4} \otimes \mathbb{C}^{7}$ quantum system. Then we give a general method to construct a set of orthogonal quantum states with minimal nonlocality in a bipartite quantum system with unequal local dimensions. Furthermore, we generalize the construction method to tripartite quantum system with unequal local dimensions, and construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb C^{d_1} \otimes \mathbb C^{d_2}\otimes \mathbb C^{d_3}$ quantum system for $5\le d_1 < d_2 < d_3$. Our work settles the construction problem of a set of orthogonal states with minimal nonlocality in both bipartite and tripartite systems with unequal local dimensions.
