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Projection based lower bounds of concurrence for multipartite quantum systems

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Abstract

We study the concurrence of arbitrary-dimensional multipartite quantum states. Analytical lower bounds of concurrence for tripartite quantum states are derived by projecting high-dimensional states to 2 ⊗ 2 ⊗ 2 substates. The results are then generalized to arbitrary multipartite quantum systems. Furthermore, the scheme enables us obtain lower bounds of concurrence for arbitrary four-partite quantum states by projecting high-dimensional states to arbitrary given lower dimensional substates. By detailed examples we show that our results improve the existing lower bounds of concurrence.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under grant Nos. 11101017, 11531004, 11726016 and 11675113, and Simons Foundation under grant No. 523868, Key Project of Beijing Municipal Commission of Education (KZ201810028042), and Beijing Natural Science Foundation (Z190005).

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China

    Hui Zhao & MeiMing Zhang

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei

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

    Shao-Ming Fei

  4. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

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  1. Hui Zhao
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  2. MeiMing Zhang
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  3. Shao-Ming Fei
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  4. Naihuan Jing
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Correspondence to Hui Zhao.

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Zhao, H., Zhang, M., Fei, SM. et al. Projection based lower bounds of concurrence for multipartite quantum systems. Int J Theor Phys 59, 1688–1698 (2020). https://doi.org/10.1007/s10773-020-04436-x

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  • DOI: https://doi.org/10.1007/s10773-020-04436-x

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