Influence Of Entanglement Degree On Strategy Selection Of Quantum Prisoner’s Dilemma In Different Noise Channels

Quantum game theory is an interdisciplinary subject that studies game theory in quantum information theory as a tool.By introducing entangled states,the strategy set of the corresponding classical game is expanded.Therefore,the dilemma in the classical game is solved.Prisoner’s dilemma is the most classical game model in game theory.At present,most of the researches on it are carried out under the closed system.However,in fact,the external environment often affects the system itself,resulting in decoherence.Therefore,under the condition of open quantum system,how quantum entanglement affects the strategy choice of prisoner’s dilemma is a important topic.Based on these,this thesis uses the relevant theories of quantum game,taking external factors into account in the prisoner’s dilemma model,and establishes the quantum prisoner’s dilemma model under different noise channels.We study the effect of entanglement on the strategy.It expands the effective scope of the application of prisoner’s dilemma model.These provide a certain scientific basis for the application of quantum game in reality.The main contents of this thesis are as follows:（1）Using the "minimum" quantization scheme and quantum game theory proposed by Eisert et al,to establish a quantum prisoner’s dilemma model under the condition of phase damping channel.We study the effect of entanglement on the strategy,it is concluded that the two entanglement values when both choose the betrayal strategy,one chooses the betrayal strategy,one chooses the quantum strategy,and then both choose the quantum strategy.Then,when there is no noise,the entanglement values are 0.532 and 0.785 respectively.When the noise is 0.5,the entanglement values are 0.889 and 1.071 respectively.When the noise is maximum,the entanglement values are 0.955 and 1.107 respectively.It is further concluded that two values of entanglement are the increasing functions of noise.（2）Under the condition of phase flip channel.We study the effect of entanglement on the strategy,it is concluded that the two entanglement values when both choose the betrayal strategy,one chooses the betrayal strategy,one chooses the quantum strategy,and then both choose the quantum strategy.Then,when there is no noise and the maximum noise,the entanglement values are 0.532 and 0.785 respectively.When the noise is 0.5,the entanglement values are 0.955 and 1.107 respectively.It is further concluded that when the noise is less than 0.5,the entanglement values are the increasing function of noise,and when the noise is greater than 0.5,the critical entanglement values are the decreasing function of noise.