Research On Related Problems Of Quantum Coin Flipping Model In Different Noise Environments

Quantum game theory is an interdisciplinary subject that applies quantum information theory to game theory.As a classic basic model,coin flipping game has attracted much attention and is one of the hot fields in the research of game theory.At present,many mathematicians study the model in a closed system,while the real world is an open system,and its evolution process must be affected by the external environment.How the external environment affects the choice of equilibrium strategy of coin flipping model is an important problem to be solved urgently.Based on this,aiming at the decoherence phenomenon caused by the coupling between the quantum system and the external environment,using the relevant theory of quantum game,this thesis establishes the multi coin quantum game model under different noise channels and the two coin quantum game model under different memory channels in the open environment,and discusses the law that the income of quantum participants,that is,the winning probability,changes with the relevant variables,It provides a theoretical basis for the multi coin game decision and the influence of memory effect on the two coin quantum game under different external environment conditions.The main contents of this thesis are as follows:(1)The single coin quantum game is extended to multi coin quantum game.The multi coin quantum game models under depolarization channel,amplitude damping channel and phase damping channel are established respectively.The income of quantum strategy participants,that is,the winning probability,is negatively correlated with the change of noise parameters and the number of coins.Then the influence of these three different channels on their income is discussed and analyzed.It is found that no matter how many coins are taken,The participant's income decreases the slowest in amplitude damped channel and the fastest in depolarized channel.(2)Aiming at the memory problem of external environmental noise channel,a two coin quantum game model based on memory depolarization channel,amplitude damping channel and phase damping channel is established.The model and the change of quantum participant's income under memory channel are analyzed.It is found that under depolarization channel and amplitude damping channel,the memory effect is positively correlated with the income of quantum participant,At this time,the memory effect can reduce the negative impact of noise on income.In the three kinds of memory noise channels,only in the amplitude damping channel,the quantum participant's income is sometimes affected by the classical participant's coin turnover probability,and only in the phase damping channel,the memory effect is sometimes negatively correlated with the quantum participant's income,even if the quantum participant's income decreases with the increase of memory intensity.