中国物理B ›› 2012, Vol. 21 ›› Issue (1): 10302-010302.doi: 10.1088/1674-1056/21/1/010302

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New theorem relating two-mode entangled tomography to two-mode Fresnel operator

谢传梅1, 范洪义2   

  1. (1)College of Physics & Material Science, Anhui University, Hefei 230039, China; Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China; (2)Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2011-07-20 修回日期:2011-08-26 出版日期:2012-01-15 发布日期:2012-01-20
  • 基金资助:
    Project supported by the Doctoral Scientific Research Startup Fund of Anhui University, China (Grant No. 33190059), the National Natural Science Foundation of China (Grant No. 10874174), and the President Foundation of Chinese Academy of Sciences.

New theorem relating two-mode entangled tomography to two-mode Fresnel operator

Xie Chuan-Mei(谢传梅)a)b)† and Fan Hong-Yi(范洪义)b)   

  1. a College of Physics & Material Science, Anhui University, Hefei 230039, China; b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2011-07-20 Revised:2011-08-26 Online:2012-01-15 Published:2012-01-20
  • Supported by:
    Project supported by the Doctoral Scientific Research Startup Fund of Anhui University, China (Grant No. 33190059), the National Natural Science Foundation of China (Grant No. 10874174), and the President Foundation of Chinese Academy of Sciences.

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摘要： Based on the Fan-Hu's formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states' wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of F2+ρF2, where F2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.

关键词: two-mode quantum tomogram, two-mode Fresnel operator, Weyl correspondence

Abstract: Based on the Fan-Hu's formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states' wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of F2+ρF2, where F2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.

Key words: two-mode quantum tomogram, two-mode Fresnel operator, Weyl correspondence

中图分类号:  (Quantum mechanics)

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73.63.Kv (Quantum dots)