Influence Of Quantum Entanglement And Quantum Noise On Quantum Games

In the past few years, quantum information science has become one ofthe frontest areas in physics and information science. Quantum mechanicsand relativity are considered as two foundations of modern physics. Therehas been a great deal of effort to extend the classical game theory into thequantum domain since it is believed that the quantum game theory may beapplicable for the study of effective quantum communication as well as for theproduction of new algorithms for quantum computers. Furthermore, variousproposals of applying quantum-like models in social sciences and economicshave been put forward.This thesis is devoted to investigating the influence of entanglement anddeeoherence on the quantum Stackelberg duopoly (QSD) game and consistsof five chapters. In chapter 1, the basic theory of the game and classic gamemodels are briefly reviewed.In chaper 2, we introduce the basic theory of quantum entanglement andquantum noise. We describe simply the definition of quantum entanglementand measure of the degree of quantum entanglement. Then, we review threetypes os quantum channels to describe quantum noise. Amplitude damping,depolarizing damping and phase damping are discussed in terms of Krausoperators, respectively.In chapter 3, we investigate the influence on the QSD game of quantumentanglement. It is shown that the first-mover advantage can be weakenedor enhanced due to the existence of entanglement for the QSD game withoutdecoherence.In chapter 4, we analyze the effects of decoherence on the QSD game underdecoherence. The influence of decoherence induced by the amplitude damping,the depolarizing damping and the phase damping are explicitly studied in theformalism of Kraus operator representations. We show that the amplitudedamping seriously affects the Nash equilibrium of the QSD game and the profits of the two players while the phase damping does not affect the Nashequilibrium and the profits of the two players. It is found that under certainconditions there exists a "critical point" of the damping parameter for theamplitude damping environment. At the "critical point" the two players havethe same moves and payoffs. The QSD game can change from the first-moveradvantage game into the follower-mover advantage game when the dampingparameter varies from the left-hand-side regime of the "critical point" to theright-hand-side regime. It is found that the presence of the damping in thedepolarizing channel always leads to the decrease of the quantities of the movesand payoffs of the two players in the QSD game. It is indicated that undercertain conditions the first-mover advantage in the QSD game can be weakeneddue to the presence of the damping in the depolarizing channel.Finally, a summary and an outlook of this thesis are given in chapter 5.