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Local distinguishability of generalized Bell states

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Abstract

We investigate the distinguishability of orthogonal generalized Bell states (GBSs) in \(d\otimes d\) system by local operations and classical communication (LOCC), where d is a prime. We show that |S| is no more than \(d+1\) for any l GBSs, i.e., \(|S|\le d+1\), where S is maximal set which is composed of pairwise noncommuting pairs in \({\varDelta } U\). If \(|S|\le d\), then the l GBSs can be distinguished by LOCC according to our main Theorem. Compared with the results (Fan in Phys Rev Lett 92:177905, 2004; Tian et al. in Phys Rev A 92:042320, 2015), our result is more general. It can determine local distinguishability of \(l (> k)\) GBSs, where k is the number of GBSs in Fan’s and Tian’s results. Only for \(|S|=d+1\), we do not find the answer. We conjecture that any l GBSs cannot be distinguished by one-way LOCC if \(|S|=d+1\). If this conjecture is right, the problem about distinguishability of GBSs with one-way LOCC is completely solved in \(d\otimes d\).

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Acknowledgements

This work is supported by NSFC (Grant Nos. 61601171, 61402148, 61701553), Project of Science and Technology Department of Henan Province of China (172102210275), Foundation of Doctor of Henan Polytechnic University (B2017-48), Natural Science Foundation of Hebei Province (F2015205114).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China

    Ying-Hui Yang, Cai-Hong Wang & Jiang-Tao Yuan

  2. School of Information, Central University of Finance and Economics, Beijing, 100081, China

    Xia Wu

  3. Mathematics and Information Science College, Hebei Normal University, Shijiazhuang, 050024, China

    Hui-Juan Zuo

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  1. Ying-Hui Yang
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Correspondence to Ying-Hui Yang.

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Yang, YH., Wang, CH., Yuan, JT. et al. Local distinguishability of generalized Bell states. Quantum Inf Process 17, 29 (2018). https://doi.org/10.1007/s11128-017-1797-2

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