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Improved lower bounds of concurrence and convex-roof extended negativity based on Bloch representations

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Abstract

Quantum entanglement plays significant roles in quantum information processing. Estimating quantum entanglement is an essential and difficult problem in the theory of quantum entanglement. We study two main measures of quantum entanglement: concurrence and convex-roof extended negativity. Based on the improved separability criterion from the Bloch representation of density matrices, we derive analytical lower bounds of the concurrence and the convex-roof extended negativity for arbitrary dimensional bipartite quantum systems. We show that these bounds are better than some of the existing ones by detailed examples.

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Acknowledgements

This work is supported by the NSFC Nos. 11775306, 11701568 and 11675113; the Fundamental Research Funds for the Central Universities Grants Nos. 19CX02050A, and 17CX02033A; the Shandong Provincial Natural Science Foundation Nos. ZR2016AQ06, and ZR2017BA019; and a project sponsored by SRF for ROCS, SEM; and NSF of Beijing under No. KZ201810028042 and No. Z190005.

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Authors and Affiliations

  1. College of the Science, China University of Petroleum, Qingdao, 266580, China

    Ming Li, Zong Wang, Jing Wang & Shuqian Shen

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

    Ming Li & Shao-ming Fei

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

    Shao-ming Fei

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  1. Ming Li
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  2. Zong Wang
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  3. Jing Wang
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  4. Shuqian Shen
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  5. Shao-ming Fei
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Correspondence to Jing Wang.

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Li, M., Wang, Z., Wang, J. et al. Improved lower bounds of concurrence and convex-roof extended negativity based on Bloch representations. Quantum Inf Process 19, 130 (2020). https://doi.org/10.1007/s11128-020-02624-6

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