中国物理B ›› 2006, Vol. 15 ›› Issue (1): 60-65.doi: 10.1088/1009-1963/15/1/010

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The effect of quantum noise on the restricted quantum game

曹帅, 方卯发   

  1. College of Physics and Information Science, Hunan Normal University,Changsha 410081, China
  • 收稿日期:2005-07-15 修回日期:2005-09-26 出版日期:2006-01-20 发布日期:2006-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10374025).

The effect of quantum noise on the restricted quantum game

Cao Shuai (曹帅), Fang Mao-Fa (方卯发)   

  1. College of Physics and Information Science, Hunan Normal University,Changsha 410081, China
  • Received:2005-07-15 Revised:2005-09-26 Online:2006-01-20 Published:2006-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10374025).

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摘要： It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of $0

关键词: entanglement, quantum game, quantum noise, Nash equilibria

Abstract: It has recently been established that quantum strategies have great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise resulting in decoherence. In this paper, we investigate the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise. Our results show that in the maximally entangled state, no Nash equilibria exist in the range of 0<p ?0.422 (p is the quantum noise parameter), while two special Nash equilibria appear in the range of 0.422<p<1. The advantage that the quantum player diminished only in the limit of maximum quantum noise. Increasing the amount of quantum noise leads to the increase of the classical player's payoff and the reduction of the quantum player's payoff, but is helpful in forming two Nash equilibria.

Key words: entanglement, quantum game, quantum noise, Nash equilibria

中图分类号:  (Decision theory and game theory)

  • 02.50.Le
03.67.Mn (Entanglement measures, witnesses, and other characterizations) 03.65.Yz (Decoherence; open systems; quantum statistical methods)