Studies On The Superiority Of The CHSH Quantum Game

Game theory is a theory that in games or gamblings, how to choose an optimal strategy for obtaining maximum benefit,which is also called strategy theory. In recent years, quantum game, combined with game theory and quantum information theory, has become a hot research topic. Most studies focused on the advantages of quantum game in cases of maximally entangled states and certain quantum operations. A few works discussed the superiority of quantum game model in the noise environment. In practice, particles may not be maximally entangled states. There maybe exist some quantum operation deviations. There often exist quantum noises in systems. Therefore, considering the above mentionded factors, it is significance to the application of quantum game.Firstly, the influences of quantum entanglement and quantum operation on the superiority of the CHSH quantum game are studied, respecitvely. It is found that when particles are in general entangled quantum states, the probability of winning for quantum strategy P is not always greater than that for classical strategycP, therefore suitable quantum operations should be chosen to satisfy that cP >P. The maximum of the probability of winning for quantum strategymaxP increases with the degree of entanglement of quantum states. For some angle regions that near the angle corresponding tomaxP, the P changes slightly. At the same time, all these studies are very meaningful for reducing the communication complexity problem that based on the CHSH game model.Secondly, the influences of quantum entanglement and quantum operation on the superiority of the Bojic CHSH quantum game and the conflicting interest CHSH game are studied, resepectively. It is found that when particles are in general entangled quantum states and suitable quantum operations are selected, the the probability of winning P(income F) with a quantum strategy is greater than that for classical strategy. In addition, in the two game models, the superiority of quantum game strategy is more apparent.Finally, the influences of four kinds of decoherences on the CHSH quantum game and the conflicting interest CHSH game are studied, respectively. In practice, quantum systems will be inevitably disturbed by environments, and the quantum system will be decoherence. It is found that the influences of the different kinds of decoherences are different for games. The winning probability P or average income F has little change when noise within a certain intensity.