Noisy non-transitive quantum games

Abstract

We study the effect of quantum noise in 3 × 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 α = 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.

Імітаційна Модель Пінг-Понг Протоколу З Парами Переплутаних Кутритів У Квантовому Каналі З Шумом

“…Дія ДПК на окремий кутрит описується більш складним оператором, ніж його дія на кубіт. Згідно з [15], ( Розглянемо тепер режим контролю підслуховування в пінг-понг протоколі з парами переплутаних кутритів для випадку, коли на передаваний кутрит діє оператор шуму (5) (рис. 2).…”

Transitivity of an entangled choice

“…Despite numerous research studies on the usefulness of quantum formalism in constructing games and algorithms [4][5][6][7][8][9][10][11][12], the issue of intransitive orders is rarely subject to analysis. For the time being, only a few papers aimed at analysing the problem have been written [13,14]. Considering the importance of intransitivity for classical games and decision theory (see section 2), one may assume that it will be important for research on characteristics of games analysed within quantum information theory.…”