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Indistinguishability of pure orthogonal product states by LOCC

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Abstract

We construct two sets of incomplete and extendible quantum pure orthogonal product states (POPS) in general bipartite high-dimensional quantum systems, which are all indistinguishable by local operations and classical communication. The first set of POPS is composed of two parts which are \(\mathcal {C}^m\otimes \mathcal {C}^{n_1}\) with \(5\le m\le n_1\) and \(\mathcal {C}^m\otimes \mathcal {C}^{n_2}\) with \(5\le m \le n_2\), where \(n_1\) is odd and \(n_2\) is even. The second one is in \(\mathcal {C}^m\otimes \mathcal {C}^n\) \((m, n\ge 4)\). Some subsets of these two sets can be extended into complete sets that local indistinguishability can be decided by noncommutativity which quantifies the quantumness of a quantum ensemble. Our study shows quantum nonlocality without entanglement.

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Acknowledgements

This work is supported by National Science Foundation of China (Nos. 61272413, 61272415, 61373158, 61472165, 61672014, 61502200), Research Fund for the Doctoral Program of Higher Education of China (No. 20134401110011), the 2016 special fund for Applied Science and Technology Development and Transformation of Major Scientific and Technological Achievements, the fund for Zhuhai City Predominant Disciplines, Guangdong Provincial Big Data Collaborative Innovation Center, Shenzhen University, the Open Project Program of the Guangdong Provincial Big Data Collaborative Innovation Center, the Natural Science Foundation of Guangdong (Nos. 2016A030313090, 2016A030313350 and 2014A030310245), the Special Funds for Science and Technology Development of Guangdong (No. 2016KZ010103), the Transformation Project of Sci-tech Achievements of SYSU, the Fundamental Research Funds for the Central Universities (No. 16lgjc83) and Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) (No. nsfc2015_180).

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Authors and Affiliations

  1. Department of Computer Science, Jinan University, Guangzhou, 510632, People’s Republic of China

    Xiaoqian Zhang, Jian Weng & Weiqi Luo

  2. Department of Mathematics, Jinan University, Guangzhou, 510632, People’s Republic of China

    Xiaoqing Tan

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  1. Xiaoqian Zhang
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  2. Jian Weng
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Correspondence to Jian Weng.

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Zhang, X., Weng, J., Tan, X. et al. Indistinguishability of pure orthogonal product states by LOCC. Quantum Inf Process 16, 168 (2017). https://doi.org/10.1007/s11128-017-1616-9

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