Quantum Games Under Quantum Noise

Game theory is a well-established discipline of applied mathematics which has found numerous applications in economy, psychology, ecology and biology. Recent development in quantum computation and quantum information theory allows to extend the scope of game theory to quantum world. So game theory and quantum theory form a new subject - quantum game theory, which is a new area of investation that has gone through rapid development during the last few years. A lot of quantum information procedure can be regarded as quantum game. So the research of quantum game is helpful for quantum algorithm and quantum communication.The thesis consists of five chapters. In chapter 1 The basic theory of the game and quantum game are briefly recalled, then some significant works of this aspect are introduced.In chapter 2, the effect of quantum noise on the restricted quantum game in which one player is restricted in classical strategic space, another in quantum strategic space and only the quantum player is affected by the quantum noise is investigated. Results show that in the maximally entangled state, the Nash equilibria do not exist in the range of 0 < p ≤ 0.422 (p is the quantum noise parameter), while two special Nash equilibria appear in the range of 0.422 < p < 1. The advantage that the quantum player diminished only in the limit of maximum quantum noise. Increasing the amount of quantum noise leads to the increase of the classical player's payoff and the reduction of the quantum player's payoff, but is helpful in forming two Nash equilibria.In chapter 3, the effect of quantum noise on the multiplayer quantum game with a certain strategic space is investigated. All players are affected by the same quantum noise at the same time. In the maximally entangle state, Results show that a special Nash equilibria exist in the range of 0 < p ≤ 0.622 (p is the quantum noise parameter), then disappear in the range of 0.622 < p ≤ 1. Increasing the amount of quantum noise leads the reduction of the quantum player's payoff.In chapter 4, Linear optics alone would suffice to implement efficient quantum computation is shown. Quantum computation circuits using coherent states as the logical qubits can be constructed from very simple linear networks, conditional measurements and coherent superposition resource states. The quantum game under quantum noise and a proposal for implementing the noisy quantum game using only linear optics are presented.In chapter 5 a summary of the work and an outlook of this aspect are given.