中国物理B ›› 2006, Vol. 15 ›› Issue (6): 1177-1183.doi: 10.1088/1009-1963/15/6/009

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Probabilistically implementing nonlocal operations between two distant qutrits

单永光, 聂建军, 曾浩生   

  1. Department of Physics, Hunan Normal University, Changsha 410081, China
  • 收稿日期:2005-08-21 修回日期:2006-03-09 出版日期:2006-06-20 发布日期:2006-06-20
  • 基金资助:
    Project supported by the National Major Fundamental Research Project, China (Grant No 2001CB309310), the National Natural Science Foundation of China (Grant Nos 10347128, 10325523 and 90203018), the Natural Science Foundation of Hunan Province (Grant No 04JJ3017), the Science Foundation for Post Doctorate of China (Grant No 2005037695), and the Scientific Research Fund of Hunan Provincial Education Bureau.

Probabilistically implementing nonlocal operations between two distant qutrits

Shan Yong-Guang (单永光), Nie Jian-Jun (聂建军), Zeng Hao-Sheng (曾浩生)   

  1. Department of Physics, Hunan Normal University, Changsha 410081, China
  • Received:2005-08-21 Revised:2006-03-09 Online:2006-06-20 Published:2006-06-20
  • Supported by:
    Project supported by the National Major Fundamental Research Project, China (Grant No 2001CB309310), the National Natural Science Foundation of China (Grant Nos 10347128, 10325523 and 90203018), the Natural Science Foundation of Hunan Province (Grant No 04JJ3017), the Science Foundation for Post Doctorate of China (Grant No 2005037695), and the Scientific Research Fund of Hunan Provincial Education Bureau.

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摘要： We propose a method to probabilistically implement a nonlocal operation, $% \exp {[}\i\xi U_{A}U_{B}{]}$, between two distant qutrits $A$ and $B$, where $% \xi \in [0,2\pi ]$ and $U_{A}$, $U_{B}$ are local unitary and Hermitian operations for qutrits $A$ and $B$ respectively. The consumptions of resource for one performance of the method are a single non-maximally entangled qutrit state and 1-trit classical communication. For a given $\xi $% , the successful probability of the method depends on the forms of both entanglement resource and Bob's partial-measurement basis. We systematically discuss the optimal successful probabilities and their corresponding conditions for three cases: adjustable entanglement resource, adjustable partial-measurement basis, adjustable entanglement resource and partial-measurement basis. It is straightforward to generalize the method for producing nonlocal unitary operations between any two $N$-level systems.

关键词: nonlocal operation, qutrit, optimal successful probability

Abstract: We propose a method to probabilistically implement a nonlocal operation, $% \exp[{\rm i}\xi U_{A}U_{B}{]}$, between two distant qutrits $A$ and $B$, where $\xi \in [0,2\pi ]$ and $U_{A}$, $U_{B}$ are local unitary and Hermitian operations for qutrits $A$ and $B$ respectively. The consumptions of resource for one performance of the method are a single non-maximally entangled qutrit state and 1-trit classical communication. For a given $\xi$ , the successful probability of the method depends on the forms of both entanglement resource and Bob's partial-measurement basis. We systematically discuss the optimal successful probabilities and their corresponding conditions for three cases: adjustable entanglement resource, adjustable partial-measurement basis, adjustable entanglement resource and partial-measurement basis. It is straightforward to generalize the method for producing nonlocal unitary operations between any two $N$-level systems.

Key words: nonlocal operation, qutrit, optimal successful probability

中图分类号:  (Quantum computation architectures and implementations)

  • 03.67.Lx
02.50.Cw (Probability theory) 03.65.Ta (Foundations of quantum mechanics; measurement theory) 03.65.Ud (Entanglement and quantum nonlocality) 03.67.Hk (Quantum communication) 03.67.Mn (Entanglement measures, witnesses, and other characterizations)