Optimization of realignment criteria and its applications for multipartite quantum states (original) (raw)

Abstract

By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix, and multiple rows and columns from vectorization of reduced density matrices, the authors of Shen (Phys. Rev. A 92: 042332, 2015) presented a family of separable criteria to improve the computable cross-norm or realignment criterion Rudolph (Phys. Rev. A 67: 032312, 2003); Chen (Quantum Inf. Comput. 3: 193-202, 2003). In this paper, we first show that these criteria achieve their optimization when the parameterized matrix is chosen to be a constant matrix. It is then proved that the optimized criterion is equivalent to the corresponding criterion with one additional row and one additional column. This reduces the computation cost, since the combined realignment matrix possesses a lower dimension. Finally, the optimized criterion is further used to achieve the separable criterion for multipartite quantum states, which, by using a numerical example, is more efficient than the corresponding previous criteria based on linear contraction methods and sequential realignment methods.

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Acknowledgements

The authors thank the referees and the editor for their invaluable comments. This work is supported by NSFC (11775306, 12075159), the Shandong Provincial Natural Science Foundation for Quantum Science (ZR2021LLZ002), and the Fundamental Research Funds for the Central Universities (19CX02050A).

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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, 266580, People’s Republic of China
    Shu-Qian Shen, Lou Chen & Ming Li
  2. College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing, 100029, People’s Republic of China
    An-Wen Hu

Authors

  1. Shu-Qian Shen
  2. Lou Chen
  3. An-Wen Hu
  4. Ming Li

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Correspondence toShu-Qian Shen.

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Shen, SQ., Chen, L., Hu, AW. et al. Optimization of realignment criteria and its applications for multipartite quantum states.Quantum Inf Process 21, 135 (2022). https://doi.org/10.1007/s11128-022-03463-3

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