Distinguishability of generalized Bell states in arbitrary dimension system via one-way local operations and classical communication

Abstract

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.