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Locally distinguishing multipartite orthogonal product states with different entanglement resource

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Abstract

Recently, entanglement-assisted state discrimination has attracted much attention. However, most of the relevant results are about the bipartite quantum states and very little is known about the multipartite case. In this paper, considering the nonlocal orthogonal product states constructed by Jiang and Xu [Phys. Rev. A 102, 032211 (2020)], we first present one protocol to locally distinguish a set of orthogonal product states in \(3\otimes 3 \otimes 3\) by using a \(2\otimes 2\) maximally entangled state. Then, we generalize the distinguishing method for the class of nonlocal of orthogonal product states in \(\otimes _{j=1}^n{\mathbb {C}}^{d_j}\), where \(n\geqslant 3, d_j\geqslant 2, j=1,2,\ldots ,n\). Furthermore, for another class of orthogonal product states in \(\otimes _{j=1}^n{\mathbb {C}}^{d_j}\), where \(n\geqslant 3, d_j\geqslant 3, j=1,2,\ldots ,n\), we prove that these states can also be distinguished by LOCC with a \(3\otimes 3\) maximally entangled state or two copies of \(2\otimes 2\) maximally entangled states. The above results can let us better understand how to use entanglement resource more efficiently in multipartite quantum systems and also reveal the phenomenon of less nonlocality with more entanglement.

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Acknowledgements

This work was supported by the NSFC (Grants No. 61901030, No. 11847210 and No. 61801126), the Beijing Natural Science Foundation (Grant No. 4194088), and the Fundamental Research Funds for the Central Universities (Grant No. 06500172).

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Zhi-Chao Zhang

  2. School of Control and Computer Engineering, North China Electric Power University, Beijing, 102206, China

    Qing-Le Wang

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  1. Zhi-Chao Zhang
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  2. Qing-Le Wang
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Correspondence to Zhi-Chao Zhang.

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Zhang, ZC., Wang, QL. Locally distinguishing multipartite orthogonal product states with different entanglement resource. Quantum Inf Process 20, 75 (2021). https://doi.org/10.1007/s11128-021-03016-0

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