Quantum Cash In A Hat Game And Its Linear Optical Implementation

With the development of quantum mechanics and quantum technologies,people gradually realize the importance of quantum physics,and it also contributes to the rise of the interdisciplinary subjects between quantum physics and many other traditional disciplines include economics,chemistry,biology and so on.Based on quantum entanglement characteristic of quantum mechanics and combined with the critical applications of classic game theory in economics,this thesis discusses the problem of quantum game from the following aspects: analysis of quantum cash in a hat game and linear optical implementation of quantum cash in a hat game.Main contributions are summarized as follows:(1)We firstly investigate the quantum cash in a hat game.Through analyzing payoffs of quantum cash in a hat game,we find that the quantum strategy space is larger than the classical one and quantum version of cash in a hat game can cease the moral hazard naturally which is very difficult to solve in classical game theory.Afterward,we discuss the influence of the degree of entanglement for initial states of quantum cash in a hat game.It is revealed that there exist two thresholds,a classical threshold γthCand a quantum threshold γthQfor γ ∈ [0,π/2].Quantum cash in a hat game still behaves `classically’when 0 γ γthCand moral hazard can be overcome when γthQ γ π/2.It should be underlined that there exists a Nash equilibrium when γthC< γ < γthQ,which is unfortunately not Pareto optimal.Finally,it is discussed that how the classical and quantum thresholds depend on the payoff distribution.(2)Furthermore,we propose a scheme to realize our quantum cash in a hat game by using linear optical elements.Different from previous optical implementations of other quantum games,we use the polarizations of two single photons to code qubits in our scheme,and nonlinear Kerr media or spatial qubits are not necessary.This scheme is easier to be realized to some degrees.The thesis concludes with a summary of our work and suggestions for future work.