Using entanglement more efficiently in distinguishing orthogonal product states by LOCC

In this paper, we mainly study the problem of locally distinguishing orthogonal product states using entanglement as a resource. We present methods to improve the previous results, presented by other authors, based on an ancillary two-qubit maximally entangled state instead of a high-dimensional entanglement ancillary resource. Concretely, we present a method to locally distinguish a set of \(2n-1\) orthogonal product states in a \(m \otimes n\) bipartite system with an ancillary two-qubit maximally entangled state, and generalize the discrimination method to orthogonal product states in even-partite system. Then, we also present a method to locally distinguish a set of \(2(n_1+n_3)-3\) orthogonal product states in a \(n_1 \otimes n_2 \otimes n_3\) tripartite system with an ancillary two-qubit maximally entangled state, and generalize the discrimination method to orthogonal product states in odd-partite system. We hope that these results can lead to a better understanding of the relationship between nonlocality and entanglement.

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