Noisy non-transitive quantum games

TL;DR

This paper investigates how different types of quantum noise affect a three-strategy quantum Rock-Scissor-Paper game, revealing that some noise channels significantly alter payoffs while preserving the game's non-transitive structure.

Contribution

It provides a detailed analysis of the impact of various quantum noise channels on a non-transitive quantum game, highlighting which channels influence payoffs and which do not.

Findings

Depolarizing noise decreases payoffs monotonically with increased noise.

Amplitude damping noise affects payoffs non-monotonically, with a minimum at alpha=0.5.

Phase damping noise does not influence the game's payoff.

Abstract

We study the effect of quantum noise in 3 by 3 entangled quantum games. By considering different noisy quantum channels we analyze that how a two-player, three-strategy Rock-Scissor-Paper game is influenced by the quantum noise. We consider the winning non-transitive strategies R, S and P such as R beats S, S beats P, and P beats R. The game behaves as a noiseless game for maximum value of the quantum noise parameter. It is seen that Alice's payoff is heavily influenced by the depolarizing noise as compared to the amplitude damping noise. Depolarizing channel causes a monotonic decrease in players payoffs as we increase the amount of of quantum noise. In case of amplitude damping channel, the Alice's payoff function reaches its minimum for alpha=0.5 and is symmetrical. This means that larger values of quantum noise influence the game weakly. On the other hand, phase damping channel does not influence the game's payoff. Furthermore, the game's Nash equilibrium and non-transitive character of the game are not affected under the influence of quantum noise.