振幅阻尼信道下量子囚徒困境模型均衡解分析

量子电子学报 ›› 2020, Vol. 37 ›› Issue (1): 70-75.

振幅阻尼信道下量子囚徒困境模型均衡解分析

杨阳,王爽,张新立

辽宁师范大学数学学院，辽宁大连 116029

收稿日期:2019-09-17 修回日期:2019-10-21 出版日期:2020-01-28 发布日期:2020-01-28
通讯作者: 杨阳 E-mail:xinli70@sohu.com
作者简介:杨阳（1996-），女，硕士，主要从事量子博弈及应用方面的研究。E-mail：601168272@qq.com
基金资助:
Supported by Education Department of Liaoning Province(辽宁省教育厅资助, LF201783613）

Equilibrium solution analysis of quantum prisoner's dilemma model in amplitude damping channel

YANG Yang, WANG Shuang, ZHANG Xinli

College of Mathematics, Liaoning Normal University, Dalian 116029, China

Received:2019-09-17 Revised:2019-10-21 Published:2020-01-28 Online:2020-01-28

摘要/Abstract

摘要： 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，得出在无记忆条件下，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，则阈值增大到0.9654，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。

关键词: 量子光学, 均衡解, 量子博弈论, 囚徒困境, 振幅阻尼信道

Abstract: The decoherence phenomena is 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. It solves the payoffs and Nash equilibrium solutions under memoryless and complete memory channels, analyzes the influence of noise strength on Nash equilibrium. It is concluded that noise has no effect on Nash equilibrium when the noise strength is less than 0.5961 under the memoryless amplitude damped channel, while the threshold value increases to 0.9654 under the complete memory condition. It explains 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. It provides certain decision-making reference for solving a feasible solution to the prisoner's dilemma in the open quantum system.

Key words: quantum optics, equilibrium solution, quantum game theory, prisoner's dilemma, amplitude-damping channel

中图分类号:

O225

杨阳王爽张新立. 振幅阻尼信道下量子囚徒困境模型均衡解分析[J]. 量子电子学报, 2020, 37(1): 70-75.

YANG Yang, WANG Shuang, ZHANG Xinli. Equilibrium solution analysis of quantum prisoner's dilemma model in amplitude damping channel[J]. Chinese Journal of Quantum Electronics, 2020, 37(1): 70-75.

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