Local unitary classification of generalized Bell state sets in C5 ⊗ C5
Local unitary classification of generalized Bell state sets in C5 ⊗ C5
复制标题
C5 中广义贝尔状态集的局部酉分类 → C5
DOI：
10.1063/5.0029164
复制
发表时间：
2021-03-01
影响因子：
1.3
通讯作者：
Mu, G. F.
中科院分区：
文献类型：
--
作者：
Wang, C. H.;Yuan, J. T.;Mu, G. F.
为了有效地研究大量的广义贝尔态，利用局域幺正等价对它们进行分类是非常重要的。例如，在C5循环乘以C5中存在C254（=12 650）个四个GBS的集合，这大大超过了在C4循环乘以C4中的C164（=1820）个四个GBS的集合，并且在没有预先分类的情况下直接探索这些集合是不可想象的。本文研究了C5圈乘C5上的GBS集的分类问题。首先，给出了GBS集的LU-等价的两个简单而有用的刻画。然后，一个特征是用来划分所有12650集的四个GBS到8个等价类，包括6个本地可区分的类和两个类，不能区分的单向本地操作和经典的通信。第二个刻画是强有力的，可以用来编写程序，利用它可以将C5圈乘C5的所有C255（=53 130）个GBS集划分为21个等价类，其中包括9个局部可区分类和12个局部不可区分类.
In order to study a large number of generalized Bell states (GBSs) efficiently, it is important to classify them by local unitary (LU) equivalence. For example, there are C254(=12 650) sets of four GBSs in C5 circle times C5, which greatly exceed the C164(=1820) sets of four GBSs in C4 circle times C4, and it is inconceivable to explore these sets directly without prior classification. In this paper, we consider the classification of GBS sets in C5 circle times C5. First, two simple and useful characterizations of LU-equivalence of GBS sets are given. Then, one characterization is used to divide all 12650 sets of four GBSs into eight equivalence classes including six locally distinguishable classes and two classes that cannot be discriminated by one-way local operations and classical communication. The second characterization is powerful and can be used to write a program, by using which all C255(=53 130) sets of five GBSs in C5 circle times C5 are divided into 21 equivalence classes including 9 locally distinguishable classes and 12 locally indistinguishable classes.