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von Neumann measurement-related matrices and the nullity condition for quantum correlation

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Abstract

We study von Neumann measurement-related matrices, and the nullity condition of quantum correlation. We investigate the properties of these matrices that are related to a von Neumann measurement. It is shown that these (m 2 − 1) × (m 2 − 1) matrices are idempotent, and have rank m − 1. These properties give rise to necessary conditions for the nullity of quantum correlations in bipartite systems. Finally, as an example we discuss quantum correlation in Bell diagonal states.

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Authors and Affiliations

  1. School of Science, Beijing Information Science and Technology University, Beijing, 100192, China

    MingJing Zhao

  2. State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, China

    Teng Ma

  3. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, China

    TingGui Zhang

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

    Shao-Ming Fei

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

    Shao-Ming Fei

Authors
  1. MingJing Zhao
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  2. Teng Ma
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  3. TingGui Zhang
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  4. Shao-Ming Fei
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Correspondence to MingJing Zhao.

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Zhao, M., Ma, T., Zhang, T. et al. von Neumann measurement-related matrices and the nullity condition for quantum correlation. Sci. China Phys. Mech. Astron. 59, 120313 (2016). https://doi.org/10.1007/s11433-016-0356-2

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  • DOI: https://doi.org/10.1007/s11433-016-0356-2

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