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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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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DOI: https://doi.org/10.1007/s11128-017-1797-2