Time dependence of Eisert–Wilkens–Lewenstein quantum game

The Eisert–Wilkens–Lewenstein (EWL) game can be used to solve the quantum prisoner’s dilemma is investigated. It is assumed that the states of the players are polarized in different directions, and the entangling gate is time dependent, with interaction strength represented by linear, sine, cosine, or exponential functions. If both players cooperate, the payoffs remain above their classical counterparts. However, if they do not cooperate, the payoff for one player increases at the expense of the other. The payoffs of both players are similar when their states are prepared with the same settings, whereas different settings for the initial states result in different payoffs. Due to the periodic nature of the interaction strength, the payoffs oscillate between their classical bounds when both initial states have the same settings. Conversely, for different initial state, the upper bounds are lower than the classical ones, while the minimum values remain above their corresponding classical payoffs.