中国物理B ›› 2009, Vol. 18 ›› Issue (6): 2129-2136.doi: 10.1088/1674-1056/18/6/004

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New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application

徐世民1, 徐兴磊1, 李洪奇1, 王继锁2   

  1. (1)Department of Physics, Heze University, Heze 274015, China;Key Laboratory of Quantum Communication and Calculation, Heze University, Heze 274015, China; (2)Department of Physics, Liaocheng University, Liaocheng 252059, China
  • 收稿日期:2008-09-07 修回日期:2008-11-01 出版日期:2009-06-20 发布日期:2009-06-20
  • 基金资助:
    Project supported by the Natural Science Foundation of Heze University of Shandong Province, China (Grant Nos XY07WL01 and XY08WL03), the University Experimental Technology Foundation of Shandong Province, China (Grant No S04W138), the Natural Science Foundation of Shandong Province of China (Grant No Y2008A16), and the National Natural Science Foundation of China (Grant No 10574060).

New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application

Xu Shi-Min(徐世民)a)b), Xu Xing-Lei(徐兴磊)a)b)†, Li Hong-Qi(李洪奇)a)b), and Wang Ji-Suo(王继锁)c)   

  1. a Department of Physics, Heze University, Heze 274015, China; b Key Laboratory of Quantum Communication and Calculation, Heze University, Heze 274015, China; c Department of Physics, Liaocheng University, Liaocheng 252059, China
  • Received:2008-09-07 Revised:2008-11-01 Online:2009-06-20 Published:2009-06-20
  • Supported by:
    Project supported by the Natural Science Foundation of Heze University of Shandong Province, China (Grant Nos XY07WL01 and XY08WL03), the University Experimental Technology Foundation of Shandong Province, China (Grant No S04W138), the Natural Science Foundation of Shandong Province of China (Grant No Y2008A16), and the National Natural Science Foundation of China (Grant No 10574060).

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摘要： We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix | ξ 1 ,ξ 2 >C,DC,D< ξ 1 ,ξ 2 | is a Radon transform of Wigner operator.

关键词: two-particle system, intermediate momentum-coordinate representation, IWOP technique

Abstract: We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product (IWOP) of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some two-body dynamic problems. Moreover, the pure-state density matrix $|\xi_1,\xi_2\rangle_{C, D\ C, D}\langle \xi_1,\xi_2|$ is a Radon transform of Wigner operator.

Key words: two-particle system, intermediate momentum-coordinate representation, IWOP technique

中图分类号:  (Entanglement and quantum nonlocality)

  • 03.65.Ud
02.10.Ud (Linear algebra) 03.67.Mn (Entanglement measures, witnesses, and other characterizations) 42.50.Dv (Quantum state engineering and measurements)