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We are considering a quantum version of the penny flip game, whoseimplementation is influenced by the environment that causes decoherence of thesystem. In order to model the decoherence we assume Markovian approximation ofopen quantum system dynamics. We focus our attention on the phase damping,amplitude damping and amplitude raising channels. Our results show that thePauli strategy is no longer a Nash equilibrium under decoherence. We attempt tooptimize the players' control pulses in the aforementioned setup to allow themto achieve higher probability of winning the game compared to the Paulistrategy.

Decoherence effects in the quantum qubit flip game using Markovian approximation