Novel methods to construct nonlocal sets of orthogonal product states in an arbitrary bipartite high-dimensional system
Novel methods to construct nonlocal sets of orthogonal product states in an arbitrary bipartite high-dimensional system
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DOI：
10.1007/s11128-021-03062-8
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发表时间：
2020-03
影响因子：
2.5
通讯作者：
Guangbao Xu;D. Jiang
中科院分区：
文献类型：
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作者：
Guangbao Xu;D. Jiang
非局域正交乘积态集（OPSs）由于其良好的性质而被广泛应用于量子协议中。在[Phys. Rev. A 101，062329（2020）]中，作者构建了一些不可扩展的产品基量子系统。我们发现，他们不可扩展的产品基础（UPB）的一个子集无法通过本地运营和经典通信（LOCC）完美区分。利用Vandermonde行列式和克雷默定则给出了该子集的非局部性的一个证明。同时，我们给出了一种新的方法来构造一个只有OPSs量子系统的非局部集。通过与已有结果的比较，我们知道这是迄今为止构造一个非局部完备集量子系统所需的最少OPS数。这意味着我们给出了在任意给定空间中构造一个可完备的非局部集合所需的最少元素数。我们的工作对于理解任意二部高维系统中局部不可区分的OPSs的结构和分类有很大的帮助。
Nonlocal sets of orthogonal product states (OPSs) are widely used in quantum protocols owing to their good property. In [Phys. Rev. A 101, 062329 (2020)], the authors constructed some unextendible product bases inquantum system for. We find that a subset of their unextendible product basis (UPB) cannot be perfectly distinguished by local operations and classical communication (LOCC). We give a proof for the nonlocality of the subset with Vandermonde determinant and Kramer’s rule. Meanwhile, we give a novel method to construct a nonlocal set with onlyOPSs inquantum system forand. By comparing the number of OPSs in our nonlocal set with that of the existing results, we know thatis the minimum number of OPSs to construct a nonlocal and completable set inquantum system so far. This means that we give the minimum number of elements to construct a completable and nonlocal set in an arbitrary given space. Our work is of great help to understand the structure and classification of locally indistinguishable OPSs in an arbitrary bipartite high-dimensional system.