The Role of Correlation in Quantum and Classical Games

TL;DR

This paper investigates the role of correlation in quantum and classical 2-player games, revealing that classical correlation often suffices to explain quantum game behaviors and that quantum advantages can be replicated classically.

Contribution

It demonstrates that simple quantum games' behaviors are driven by classical correlation and that quantum games with entanglement can be simulated by classical models.

Findings

Classical correlation explains simple quantum game behaviors.

Quantum games with entanglement can be simulated by classical channels.

Enhanced payoffs are due to classical correlation, not quantum entanglement.

Abstract

We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these simple quantum games are not sensitive to the quantum part of the correlation. In these games played with quantum objects it is possible to transform a game such as Prisoner's Dilemma into the game of Chicken. We show that this behaviour, and the associated enhanced equilibrium payoff over playing the game with quantum objects in non-entangled states, is entirely due to the classical part of the correlation. Generalizing these games to the pure strategy 2-player quantum game where the players have finite strategy sets and a projective joint measurement is made on the output state produced by the players, we show that a given quantum game of this form can always be reproduced by a classical model, such as a communication channel. Where entanglement is a feature of the these 2-player quantum games the matrix of expected outcomes for the players can be reproduced by a classical channel with correlated noise.