The effect of quantum memory on quantum games

TL;DR

This paper explores how quantum memory influences the outcomes of quantum games, demonstrating that quantum players generally gain advantages over classical players across various noisy channels and entanglement levels.

Contribution

It introduces a generalized quantization scheme to analyze quantum games with correlated noise and examines the impact of memory on game equilibria and player advantages.

Findings

Quantum players outperform classical players in all maximally entangled cases.

Quantum advantage persists in certain non-maximally entangled scenarios.

Nash equilibria remain unchanged despite the presence of memory effects.

Abstract

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maximally entangled case. However, the quantum player can also outperform the classical player for subsequent cases that can be noted in the case of the Battle of the Sexes game. It can be seen that the Nash equilibria do not change for all the three games under the effect of memory.