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

Abstract

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

CLC Number:

O225

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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