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Detection of genuine tripartite entanglement based on Bloch representation of density matrices

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Abstract

We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation tensors in the Bloch representation of the simplified density matrices. Using these special matrices, we obtain new criteria for genuine multipartite entanglement. Detail examples show that our criteria are able to detect more tripartite entangled and genuine tripartite entangled states than some existing criteria.

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All data generated or analyzed during this study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under grant nos. 11101017, 11531004, 11726016 and 12075159, Simons Foundation under grant no. 523868, Beijing Natural Science Foundation (grant no. Z190005), Academy for Multidisciplinary Studies, Capital Normal University, and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology (no. SIQSE202001), the National Natural Science Foundation of China under grant nos. 12126351 and 12171044 and the Academician Innovation Platform of Hainan Province.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Hui Zhao & Yu-Qiu Liu

  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 & Shao-Ming Fei

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

    Shao-Ming Fei

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  1. Hui Zhao
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  2. Yu-Qiu Liu
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  3. Naihuan Jing
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  5. Shao-Ming Fei
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Correspondence to Hui Zhao.

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Zhao, H., Liu, YQ., Jing, N. et al. Detection of genuine tripartite entanglement based on Bloch representation of density matrices. Quantum Inf Process 21, 116 (2022). https://doi.org/10.1007/s11128-022-03456-2

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