中国物理B ›› 2010, Vol. 19 ›› Issue (7): 70301-070301.doi: 10.1088/1674-1056/19/7/070301

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New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

范洪义, 袁洪春   

  1. Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China
  • 出版日期:2010-07-15 发布日期:2010-07-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174) as well as the President Foundation of Chinese Academy of Sciences.

New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

Fan Hong-Yi (范洪义), Yuan Hong-Chun (袁洪春)   

  1. Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Online:2010-07-15 Published:2010-07-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174) as well as the President Foundation of Chinese Academy of Sciences.

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摘要： As a natural and important extension of Fan's paper (Fan Hong-Yi 2010 Chin. Phys. B 19 040305) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator Δ ( μ,v ) (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to ( a1+-a2) and (a1+a2+) can be solved and the contents of phase space quantum mechanics can be enriched, where ai,ai+ are bosonic creation and annihilation operators, respectively.

Abstract: As a natural and important extension of Fan's paper (Fan Hong-Yi 2010 Chin. Phys. B 19 040305) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator $\Delta(\mu, \nu)$  (in its entangled form) in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to $(a^\dagger_1-a_2)$ and $(a_1+a^\dagger_2)$ can be solved and the contents of phase space quantum mechanics can be enriched, where $a_i$, $a_i^\dagger$ are bosonic creation and annihilation operators, respectively.

Key words: Wigner operator in entangled form, Weyl ordering, two-fold complex integration transformation

中图分类号:  (Entanglement and quantum nonlocality)

  • 03.65.Ud
03.67.Mn (Entanglement measures, witnesses, and other characterizations) 02.30.Tb (Operator theory) 03.65.Fd (Algebraic methods) 02.30.Zz (Inverse problems) 02.30.Uu (Integral transforms)