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A multipartite entanglement measure based on coefficient matrices

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Abstract

The quantification of quantum entanglement has been extensively studied in past years. However, many existing entanglement measures are difficult to calculate. And lots of them are introduced only for bipartite system or only for the systems constituted by qubits. In this paper, we propose an entanglement measure for multipartite system based on vector lengths and the angles between vectors of the coefficient matrices. Our entanglement measure is simple and feasible, with a remarkable geometric meaning. Furthermore, we prove that our entanglement measure satisfies the three necessary conditions which are required for any entanglement measure: (1) It vanishes if and only if the state is (fully) separable; (2) it remains invariant under local unitary transformations; and (3) it cannot increase under local operation and classical communication. Finally, we apply our entanglement measure on some computational examples. It demonstrates that our entanglement measure is capable of dealing with quantum pure states with arbitrary dimensions and parties. Meanwhile, because it only needs to compute the vector lengths and the angles between vectors of every bipartition coefficient matrix, our entanglement measure is easy to calculate.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 61272175.

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Authors and Affiliations

  1. Big Data Research Center, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Chao Zhao & Guo-wu Yang

  2. Synopsys Inc., Mountain View, CA, 94043, USA

    William N. N. Hung

  3. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Xiao-yu Li

Authors
  1. Chao Zhao
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  2. Guo-wu Yang
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  3. William N. N. Hung
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  4. Xiao-yu Li
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Correspondence to Chao Zhao.

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Zhao, C., Yang, Gw., Hung, W.N.N. et al. A multipartite entanglement measure based on coefficient matrices. Quantum Inf Process 14, 2861–2881 (2015). https://doi.org/10.1007/s11128-015-1023-z

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  • DOI: https://doi.org/10.1007/s11128-015-1023-z

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