论文标题
在任意多部分量子系统中的正交产品状态的非本地集合
Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system
论文作者
论文摘要
最近，人们对非局部多部分正交产品状态的结构引起了很多关注。在现有结果中，有些在结构上相对复杂，而另一些则具有许多约束条件。在本文中，我们首先提供了一种简单的方法，以$ \ otimes_ {j = 1}^{n} \ Mathbb {c}^{d} $ for $ d \ geq 2 $构造非本地的正交产品状态。然后，我们为通过我们的方法构建的集合的局部不可区分提供了巧妙的证据。根据这种施工方法的特征，我们在同一量子系统中获得了较少状态的非本地套装的新结构。此外，我们将这两个结果推广到更通用的$ \ otimes_ {i = 1}^{n} \ Mathbb {c}^{d_ {J}} $ Quantum System for $ d_ {J} {J} \ geq 2 $。与现有结果相比，由我们方法构建的多部分正交产品状态的非本地集合具有较少的元素，并且更简单。
Recently, much attention have been paid to the constructions of nonlocal multipartite orthogonal product states. Among the existing results, some are relatively complex in structure while others have many constraint conditions. In this paper, we firstly give a simple method to construct a nonlocal set of orthogonal product states in $\otimes_{j=1}^{n}\mathbb{C}^{d}$ for $d\geq 2$. Then we give an ingenious proof for local indistinguishability of the set constructed by our method. According to the characteristics of this construction method, we get a new construction of nonlocal set with fewer states in the same quantum system. Furthermore, we generalize these two results to a more general $\otimes_{i=1}^{n}\mathbb{C}^{d_{j}}$ quantum system for $d_{j}\geq 2$. Compared with the existing results, the nonlocal set of multipartite orthogonal product states constructed by our method has fewer elements and is more simpler.
