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The local indistinguishability of multipartite product states

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Abstract

We study the perfectly local indistinguishability of multipartite product states. Firstly, we follow the method of Zhang et al. (Phys Rev A 93:012314, 2016) to give another more concise set of \(2n-1\) orthogonal product states in \({\mathbb {C}}^m\otimes {\mathbb {C}}^n\) \((4\le m\le n)\) which can not be distinguished by local operations and classical communication. Then we use the three-dimensional cubes to present some product states which give us an intuitive view on how to construct locally indistinguishable product states in tripartite quantum systems. At last, we give an explicit construction of locally indistinguishable orthogonal product states for general multipartite systems.

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Acknowledgements

This work is supported by NSFC (Grant Nos. 11475178, 11571119, 11275131).

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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Yan-Ling Wang & Zhu-Jun Zheng

  2. Department of Mathematics, Tsinghua University, Beijing, 100084, People’s Republic of China

    Mao-Sheng Li

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People’s Republic of China

    Shao-Ming Fei

  4. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei

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  1. Yan-Ling Wang
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  2. Mao-Sheng Li
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  3. Zhu-Jun Zheng
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  4. Shao-Ming Fei
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Correspondence to Zhu-Jun Zheng.

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Wang, YL., Li, MS., Zheng, ZJ. et al. The local indistinguishability of multipartite product states. Quantum Inf Process 16, 5 (2017). https://doi.org/10.1007/s11128-016-1477-7

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  • DOI: https://doi.org/10.1007/s11128-016-1477-7

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