Implementing Quantum Prisoner Dilemma via Different Classes of Entangled and Separable States

Abstract The possibility of implementing the Prisoner's Dilemma game using different classes of initial states between the players is discussed. Different behaviors of the payoffs have been exhibited, may it increases, decreases or fixed. These behaviors depend on the used initial state either maximum/partial entangled, the chosen entangling gate, and the strategies employed by each player. The increased payoff is displayed when the players adopt different defect strategies, while the fixed payoff is shown when both players apply the same defect strategy. The maximum bounds of the payoff can be attained if the players initially share a maximum entangled state. The maximum /minimum fixed payoff depends on the used entangling gate, where the maximum one is shown if the players send their final states to entangling gate. It is shown that, the nature of the payoff, whether stationary, increasing or decreasing is contingent upon the polarization of the initial state and the used defect strategy. However, if both states are polarized on the same axis direction, the predicted maximum payoff is smaller than that obtained if the initial state are polarized in different polarization of the same axis. Therefore, the initial state settings, entangling parameter and the choice of the defect strategy can be used as control tools to maximize/minimize the obtained payoff.