中国物理B ›› 2010, Vol. 19 ›› Issue (12): 120303-120303.doi: 10.1088/1674-1056/19/12/120303

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Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

姜年权1, 吕翠红2, 范洪义2   

  1. (1)College of Physics and Electronic Information, Wenzhou University, Wenzhou 325035, China; (2)Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2010-05-11 修回日期:2010-07-28 出版日期:2010-12-15 发布日期:2010-12-15
  • 基金资助:
    Project supported by the Specialized Research Fund for Doctoral Program of High Education of China, and the National Natural Science Foundation of China (Grant Nos. 10874174 and 10947017/A05).

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

LÜ Cui-Hong(吕翠红)a), Fan Hong-Yi(范洪义) a), and Jiang Nian-Quan(姜年权)b)†ger   

  1. a Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China; b College of Physics and Electronic Information, Wenzhou University, Wenzhou 325035, China
  • Received:2010-05-11 Revised:2010-07-28 Online:2010-12-15 Published:2010-12-15
  • Supported by:
    Project supported by the Specialized Research Fund for Doctoral Program of High Education of China, and the National Natural Science Foundation of China (Grant Nos. 10874174 and 10947017/A05).

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摘要： We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation (EFFT) and derive the transformation kernel. The EFFT's additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.

Abstract: We newly construct two mutually-conjugate tripartite entangled state representations, based on which we propose the formulation of three-mode entangled fractional Fourier transformation (EFFT) and derive the transformation kernel. The EFFT's additivity property is proved and the eigenmode of EFFT is derived. As an application, we calculate the EFFT of the three-mode squeezed vacuum state.

Key words: tripartite entangled state, three-mode entangled fractional Fourier transformation, the technique of integral within an ordered product of operators

中图分类号:  (Linear algebra)

  • 02.10.Ud
02.30.Nw (Fourier analysis) 02.30.Uu (Integral transforms) 03.65.Fd (Algebraic methods) 03.65.Ud (Entanglement and quantum nonlocality)