针对开放量子系统中外部环境对系统本身造成影响而出现的退相干现象,利用量子博弈 相关理论,通过EWL量子化方案,建立了振幅阻尼信道条件下的量子囚徒困境博弈模型。在无记忆与完全记忆两种情形下,求出了 模型的收益与纳什均衡解,分析了噪音强度对纳什均衡解的影响。结果表明在无记忆条件下,当噪音强度小于阈值0.5961时,噪音 对纳什均衡没有影响;而在完全记忆条件下,阈值增大到0.9654。这说明振幅阻尼信道在完全记忆比无记忆条件下的纳什均衡解更 趋于稳定,更不易受外界环境的影响,为开放量子系统下提出解决囚徒困境的可行性方案提供了一定的决策参考依据。

Regarding the decoherence phenomena caused by some factors of external environment in an open quantum system, a quantum prisoner dilemma game model is established under amplitude channels by using EWL quantization scheme based on quantum game theory. The payoffs and Nash equilibrium solutions are obtained both in memoryless and complete memory channels, and the influence of noise strength on Nash equilibrium is also analyzed. It is found that noise has no effect on Nash equilibrium when the noise strength is less than 0.5961 under the memoryless amplitude damping channel, while the threshold value increases to 0.9654 under the complete memory condition. It indicates that the Nash equilibrium under the complete memory tends to be more stable and less susceptible to the influence of external environment than that under the memoryless condition, which provides a certain reference for decision-making of a feasible solution to the prisoner’s dilemma in the open quantum system.