Determining Quantum Correlation through Nash Equilibria in Constant-Sum Games

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.