Quantum Games under Decoherence

Quantum systems are easily influenced by ambient environments. Decoherence is generated by system interaction with external environment. In this paper, we analyse the effects of decoherence on quantum games with Eisert-Wilkens-Lewenstein (EWL) (Eisert et al., Phys. Rev. Lett. 83(15), 3077 1999) and Marinatto-Weber (MW) (Marinatto and Weber, Phys. Lett. A 272, 291 2000) schemes. Firstly, referring to the analytical approach that was introduced by Eisert et al. (Phys. Rev. Lett. 83(15), 3077 1999), we analyse the effects of decoherence on quantum Chicken game by considering different traditional noisy channels. We investigate the Nash equilibria and changes of payoff in specific two-parameter strategy set for maximally entangled initial states. We find that the Nash equilibria are different in different noisy channels. Since Unruh effect produces a decoherence-like effect and can be perceived as a quantum noise channel (Omkar et al., arXiv:1408.1477v1), with the same two parameter strategy set, we investigate the influences of decoherence generated by the Unruh effect on three-player quantum Prisoners’ Dilemma, the non-zero sum symmetric multiplayer quantum game both for unentangled and entangled initial states. We discuss the effect of the acceleration of noninertial frames on the the game’s properties such as payoffs, symmetry, Nash equilibrium, Pareto optimal, dominant strategy, etc. Finally, we study the decoherent influences of correlated noise and Unruh effect on quantum Stackelberg duopoly for entangled and unentangled initial states with the depolarizing channel. Our investigations show that under the influence of correlated depolarizing channel and acceleration in noninertial frame, some critical points exist for an unentangled initial state at which firms get equal payoffs and the game becomes a follower advantage game. It is shown that the game is always a leader advantage game for a maximally entangled initial state and there appear some points at which the payoffs become zero.