We investigate the distinguishability of generalized Bell states (GBSs) in arbitrary dimension system by one-way local operations and classical communication (LOCC). Firstly, by analyzing three local unitary transformations, we define two concepts for each set \(\mathcal {L}\) of GBSs, i.e., an admissible solutions set \(\mathcal {S}_{\mathcal {A}}\) and a genuinely nonadmissible solutions set \(\mathcal {S}_{\mathcal {L}}\). Then, we show that a set \({\mathcal {L}}\) of any GBSs can be distinguished by one-way LOCC if \({\mathcal {S}}_{\mathcal {A}}\backslash {\mathcal {S}}_{\mathcal {L}}\) is nonempty. Fan’s and Wang et al.’s results (Phys Rev Lett 92:177905, 2004: Phys Rev A 99:022307, 2019) can be covered by our result. Comparing with Wang et al.’s result, our successful ratio of local distinguishability improves markedly, especially for even dimension system. In some cases, it can increase by nearly \(42\%\). However, there are still some cases where our method cannot work. For the uncovered cases, we define an uncovered set and present that there is no method which is more powerful than ours for local discrimination of GBSs if the uncovered set is a subset of the different set of GBSs.

我们通过单向本地操作和经典通信（LOCC）研究了任意维度系统中广义贝尔状态（GBS）的可区分性。首先，通过分析三个局部unit变换，我们为GBS的每个集合\（\ mathcal {L} \）定义了两个概念，即，一个可接受的解集\（\ mathcal {S} _ {\ mathcal {A}} \ ）和真正不允许的解决方案集\（\ mathcal {S} _ {\ mathcal {L}} \）。然后，我们证明，如果\（{\ mathcal {S}} _ {\ mathcal {A}} \\反斜杠{可以用单向LOCC来区分任何GBS的\\ {{\ mathcal {L}} \\ } \ mathcal {S}} _ {\ mathcal {L}} \）是非空的。Fan和Wang等人的结果（Phys Rev Lett 92：177905，2004：Phys Rev A 99：022307，2019）可以被我们的结果覆盖。与Wang等人的结果相比，我们局部可分辨性的成功比率显着提高，尤其是对于偶数维系统。在某些情况下，它可以增加近\（42 \％\）。但是，在某些情况下，我们的方法无效。对于未发现的案例，我们定义了一个未发现的集合，并且提出了一种方法，如果该未发现的集合是GBS的不同集合的子集，则没有一种方法比我们的方法更强大。