联合退相位噪声下量子囚徒困境纳什均衡分析  

Analysis of Nash Equilibrium of Quantum Prisoner′s Dilemma with Collective-dephasing Noise Channel

作　　者：马思佳 张舒宁 王奕涵 张新立[1] MA Sijia;ZHANG Shuning;WANG Yihan;ZHANG Xinli(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《复杂系统与复杂性科学》2023年第2期68-73,80,共7页Complex Systems and Complexity Science

基　　金：教育部人文社科规划项目(21YJA630116)。

摘　　要：为讨论量子囚徒困境模型在联合退相位噪声信道影响下纳什均衡策略情况,将联合退相位噪声引入到量子博弈中,通过MW量子化方案对囚徒困境博弈模型进行量子化,建立了联合退相位噪声信道下的量子囚徒困境博弈模型。通过讨论发现,在最大纠缠的条件下,参与者的收益关于噪声参数呈现出周期性的变化,且在同一周期内,随着噪声参数的增长,量子囚徒困境在不同的噪声区间出现了存在唯一纯量子纳什均衡解、两个纯量子纳什均衡解和没有纯量子的纳什均衡解的情况,在没有纯量子均衡解的两个噪声区间中,参与者会陷入类似于石头剪刀布的循环之中。说明在联合退相位噪声信道影响下,当噪声参数属于特定噪声区间时,参与者可以达成纳什均衡。To discuss the Nash equilibrium strategy of the quantum prisoner's dilemma model under the influence of collective-dephasing noise channel,will collective-dephasing noise is introduced into the quantum game back,by MW quantization scheme to quantization of the prisoner's dilemma game,and a prisoner’s dilemma game under the effect of collective-dephasing noise is constructed.It is found that under the condition of the maximally entangle,each player’s payoff function shows periodicity about the parameter of the noise.And in the same period,along with the increase of the noise parameter,there is the unique pure quantum Nash equilibrium,two different pure quantum Nash equilibriums,and no pure quantum Nash equilibrium in different intervals.In the two noise intervals without a pure quantum Nash equilibrium,players were caught in a rock-paper-scissors loop.It shows that under the influence of collective-dephasing noise channel,players can reach Nash equilibrium when the noise parameters are in a specific interval.

关 键 词：量子博弈论 联合退相位噪声 囚徒困境 纳什均衡 

分 类 号：O413[理学—理论物理] O225[理学—物理]