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连续纠缠态表象的几种Schmidt分解、物理意义与应用

范洪义 李学超

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连续纠缠态表象的几种Schmidt分解、物理意义与应用

范洪义, 李学超

The physical significances and applications of Schmidt decompositions of continuum bipartile entangled state representation

Fan Hong-Yi, Li Xue-Chao
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  • 在两粒子连续纠缠态表象|η>的基础上分别导出了此纠缠态在坐标、 动量表象和粒子数表象中的Schmidt分解, 阐述了其物理意义.并且, 用|η>的Schmidt分解直接给出单模压缩算符对纠缠态的作用结果、 双模平移算符的纠缠态表象以及平移算符在Fock空间的矩阵元. 文章的讨论可以推广到多粒子连续纠缠态情形.
    According to the continuum bipartite entangled state representation |η> we derive the Schmidt decomposition of |η>, respectively in the coordinate representation, momentum representation and the particle number representation, and explain their physical significances. As the applications of the Schmidt decomposition, we directly derive the action of the single-mode squeeze operator on |η>, the two-mode squeeze operator's entangled state representation, as well as the matrix element of displacement operator in the Fock space. Generalization of our discussion in this paper to the multipartite entangled state cases is feasible.
    • 基金项目: 国家自然科学基金(批准号: 10874174)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10874174).
    [1]

    Dirac P A M 1930 The Principles of Quantum Mechanics (Oxford:Clarendon Press)

    [2]

    Glauber R 1963 J. Phys. Rev. 130 2529

    [3]

    Glauber R 1963 J. Phys. Rev. 131 2766

    [4]

    Reed M D, DiCarlo L, Nigg S E, Sun L, Frunzio L, Girvin S M, Schoelkopf R J 2012 Nature 482 382

    [5]

    Li P B, Gao S Y, Li F L 2012 Phys. Rev. A 85 014303

    [6]

    Cheng G L, Chen A X, Zhong W X 2011 Opt. Commun. 284 4028

    [7]

    Hou S Y, Yang K 2011 Chin. Phys. Lett. 28 064203

    [8]

    Hulya Y A, Alessio S 2011 Phys. Lett. A 375 1864

    [9]

    Meng X G, Wang J S, Liang B L 2011 Chin. Phys. B 20 050303

    [10]

    Fan H Y, Klauder J R 1994 Phys. Rev. A 49 70

    [11]

    Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777

    [12]

    Fan H Y, Fan Yue 1996 Phys. Rev. A 54 958

  • [1]

    Dirac P A M 1930 The Principles of Quantum Mechanics (Oxford:Clarendon Press)

    [2]

    Glauber R 1963 J. Phys. Rev. 130 2529

    [3]

    Glauber R 1963 J. Phys. Rev. 131 2766

    [4]

    Reed M D, DiCarlo L, Nigg S E, Sun L, Frunzio L, Girvin S M, Schoelkopf R J 2012 Nature 482 382

    [5]

    Li P B, Gao S Y, Li F L 2012 Phys. Rev. A 85 014303

    [6]

    Cheng G L, Chen A X, Zhong W X 2011 Opt. Commun. 284 4028

    [7]

    Hou S Y, Yang K 2011 Chin. Phys. Lett. 28 064203

    [8]

    Hulya Y A, Alessio S 2011 Phys. Lett. A 375 1864

    [9]

    Meng X G, Wang J S, Liang B L 2011 Chin. Phys. B 20 050303

    [10]

    Fan H Y, Klauder J R 1994 Phys. Rev. A 49 70

    [11]

    Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777

    [12]

    Fan H Y, Fan Yue 1996 Phys. Rev. A 54 958

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  • 文章访问数:  7715
  • PDF下载量:  743
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-02-25
  • 修回日期:  2012-04-19
  • 刊出日期:  2012-10-05

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