Determining Quantum Correlation through Nash Equilibria in Constant-Sum Games

TL;DR

This paper demonstrates that Nash equilibria in a specially designed quantum Bayesian game can serve as a practical mechanism to witness and determine quantum correlations, providing a new approach to understanding quantum effects.

Contribution

It introduces a novel quantum Bayesian game framework where pure strategy Nash equilibria can detect quantum correlations, highlighting the sufficiency of this method.

Findings

Pure strategy Nash equilibria can witness quantum correlations.

Mixed strategies are only necessary for quantum correlation detection.

The Bayesian game framework provides a sufficient condition for quantum effect detection.

Abstract

Quantum game theory has emerged as a promising candidate to further the understanding of quantum correlations. Motivated by this, it is demonstrated that pure strategy Nash equilibria can be utilised as a mechanism to witness and determine quantum correlation. By combining quantum theory with Bayesian game theory, a constant-sum game is designed in which the players are competing against each other, and crucially gain at the other player's expense. Subsequently, it is found that mixed strategy Nash equilibria are only necessary when considering quantum correlation for the designed game. This reveals that a Bayesian game-theoretic framework yields a sufficient condition in which to detect quantum effects.