Construnctions of LOCC indistinguishable set of generalized Bell states
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In this paper, we mainly consider the local indistinguishability of the set of mutually orthogonal bipartite generalized Bell states (GBSs). We construct small sets of GBSs with cardinality smaller than d which are not distinguished by one-way local operations and classical communication (1-LOCC) in d⊗ d. The constructions, based on linear system and Vandermonde matrix, is simple and effective. The results give a unified upper bound for the minimum cardinality of 1-LOCC indistinguishable set of GBSs, and greatly improve previous results in [Zhang et al., Phys. Rev. A 91, 012329 (2015); Wang et al., Quantum Inf. Process. 15, 1661 (2016)]. The case that d is odd of the results also shows that the set of 4 GBSs in 5⊗ 5 in [Fan, Phys. Rev. A 75, 014305 (2007)] is indeed a 1-LOCC indistinguishable set which can not be distinguished by Fan's method.
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