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Separability Criterion for Arbitrary Multipartite Pure State Based on the Rank of Reduced Density Matrix

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Abstract

Nowadays, there are plenty of separability criteria which are used to detect entanglement. Many of them are limited to apply for some cases. In this paper, we propose a separability criterion for arbitrary multipartite pure state which is based on the rank of reduced density matrix. It is proved that the rank of reduced density matrices of a multipartite state is closely related to entanglement. In fact it can be used to characterize entanglement. Our separability criterion is a necessary and sufficient condition for detecting entanglement. Furthermore, it is able to help us find the completely separable form of a multipartite pure state according to some explicit examples. Finally it demonstrates that our method are more suitable for some specific case. Our separability criterion are simple to understand and it is operational.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant (No. 61272175, 61572109).

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Authors and Affiliations

  1. Big Data Research Center, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Chao Zhao & Guo-wu Yang

  2. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Xiao-yu Li

Authors
  1. Chao Zhao
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  2. Guo-wu Yang
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  3. Xiao-yu Li
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Correspondence to Chao Zhao.

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Zhao, C., Yang, Gw. & Li, Xy. Separability Criterion for Arbitrary Multipartite Pure State Based on the Rank of Reduced Density Matrix. Int J Theor Phys 55, 3816–3826 (2016). https://doi.org/10.1007/s10773-016-3011-1

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  • DOI: https://doi.org/10.1007/s10773-016-3011-1

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