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Separability criteria based on Bloch representation of density matrices

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Abstract

We study separability criteria in multipartite quantum systems of arbitrary dimensions by using the Bloch representation of density matrices. We first derive the norms of the correlation tensors and obtain the necessary conditions for separability under partition of tripartite and four-partite quantum states. Moreover, based on the norms of the correlation tensors, we obtain the separability criteria by matrix method. Using detailed examples, our results are seen to be able to detect more entangled states than previous studies. Finally, necessary conditions of separability for multipartite systems are given under arbitrary partition.

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Acknowledgements

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).

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Authors and Affiliations

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

    Hui Zhao & Mei-Ming Zhang

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

    NaiHuan Jing

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

    Zhi-Xi Wang

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  1. Hui Zhao
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  2. Mei-Ming Zhang
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  3. NaiHuan Jing
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  4. Zhi-Xi Wang
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Correspondence to Hui Zhao.

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Zhao, H., Zhang, MM., Jing, N. et al. Separability criteria based on Bloch representation of density matrices. Quantum Inf Process 19, 14 (2020). https://doi.org/10.1007/s11128-019-2504-2

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