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Concrete Representation and Separability Criteria for Symmetric Quantum State

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Abstract

Using the typical generators of the special unitary groups S U(2), the concrete representation of symmetric quantum state is established, then the relations satisfied by those coefficients in the representation are presented. Based on the representation of density matrix, the PPT criterion and CCNR criterion are proved to be equivalent on judging the separability of symmetric quantum states. Moreover, it is showed that the matrix Γ ρ of symmetric quantum state only has five efficient entries, thus the calculation of ∥Γ ρ ∥ is simplified. Finally, the quantitative expressions of real symmetric quantum state under the ∥Γ ρ ∥ separability criterion are obtained.

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Authors and Affiliations

  1. Department of Mathematics, Yanbian University, Yanji, JiLin, 133002, People’s Republic of China

    Chang’e Li, Yuanhong Tao, Jun Zhang, Linsong Li & Hua Nan

Authors
  1. Chang’e Li
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  2. Yuanhong Tao
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  3. Jun Zhang
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  4. Linsong Li
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  5. Hua Nan
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Corresponding author

Correspondence to Yuanhong Tao.

Additional information

Y. Tao was supported by Natural Science Foundation of China (11361065); the Natural Science Foundation of Jilin Province(201215239).

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Li, C., Tao, Y., Zhang, J. et al. Concrete Representation and Separability Criteria for Symmetric Quantum State. Int J Theor Phys 53, 2923–2930 (2014). https://doi.org/10.1007/s10773-014-2090-0

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  • DOI: https://doi.org/10.1007/s10773-014-2090-0

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