论文标题
在任意双方高维系统中构建非局部量态的非本地产品态的新方法
Novel methods to construct nonlocal sets of orthogonal product states in arbitrary bipartite high-dimensional system
论文作者
论文摘要
非定位的正交产品状态（OPSS）的非局部集集已广泛用于量子协议中，这是由于其良好的特性。因此，尽管这是一个困难的问题，但人们对如何构建非本地的正交产品状态的关注很大。在本文中，我们提出了一种新颖的通用方法，用于在$ \ mathbb {c}^{d} \ otimes \ mathbb {c}^{d} $ for $ d \ geq3 $中构建一组非本地的正交产品状态。我们为这些产品状态的当地没有可区分性提供了巧妙的证据。由我们的方法构建的一组产品状态具有很好的结构。随后，我们在$ \ mathbb {c}^{d} \ otimes \ mathbb {c}^{d} $ for $ d \ geq3 $中为$ \ mathbb {c}^{d} \ otimes \ otimes \ otimes \ otimes \ otimes \ otimes \ otimes \ otimes \ otimes \ otimes \ otimes {c}^{c}^{c}^{c}^{d} $。另一方面，我们提出了两种$ \ mathbb {c}^{m}^{m} \ otimes \ Mathbb {c}^{n} $中的非局部操作集的构造方法，其中$ m \ geq3 $和$ n \ geq3。我们的工作非常有助于了解本地不可分割的OPS的结构和分类。
Nonlocal sets of orthogonal product states (OPSs) are widely used in quantum protocols owing to their good property. Thus a lot of attention are paid to how to construct a nonlocal set of orthogonal product states though it is a difficult problem. In this paper, we propose a novel general method to construct a nonlocal set of orthogonal product states in $\mathbb{C}^{d} \otimes \mathbb{C}^{d}$ for $d\geq3$. We give an ingenious proof for the local indistinguishability of those product states. The set of product states, which are constructed by our method, has a very good structure. Subsequently, we give a construction of nonlocal set of OPSs with smaller members in $\mathbb{C}^{d} \otimes \mathbb{C}^{d}$ for $d\geq3$. On the other hand, we present two construction methods of nonlocal sets of OPSs in $\mathbb{C}^{m} \otimes \mathbb{C}^{n}$, where $m\geq3$ and $n\geq3.$ Furthermore, we propose the concept of isomorphism for two nonlocal sets of OPSs. Our work is of great help to understand the structure and classification of locally indistinguishable OPSs.
