Using entanglement more efficiently in distinguishing orthogonal product states by LOCC
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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.
This work was supported by NSFC (Grant No. 11505042, No. 61672110, No. 61572081, No. 61671082, No. 11247310 and No. 11847210), Guangdong Province Outstanding Young Teachers Training Program (Grant No. YQ2015113), the Postdoctoral Innovation Talent Support Program of China (Grant No. BX20180042), the China Postdoctoral Science Foundation (Grant No. 2018M640070), the Foundation for Distinguished Young Talents in Higher Education of Guangdong (Grants No. 2012LYM_0096, No. 2018KQNCX157), the Beijing Natural Science Foundation (Grant No. 4194088).