Initial State Time-Dependent Quantum Game

The possibility of implementing a time dependent version of Eisert, Wilkens, and Lewenstein (EWL), quantum game is discussed. It is assumed that the players initial states are time dependent, while the entangling quantum gate either time dependent or independent during the game. The obtained results shows that the players payoff depend on their initial state, while The time-independent entangling gate has a minor impact on the game compared to its time-dependent counterpart. However, one can improve the lower bounds of the payoffs by using time dependent gate. Moreover, the exponential form of the entangling power is more powerful than the linear one, where the payoffs are much better. However, the maximum potential rewards in this game may be lower than those attainable in the classical game, the minimum guaranteed outcomes are much better.