Quantum advantage beyond entanglement in Bayesian game theory

Abstract

Quantum discord has been utilised in order to find quantum advantage in an extension of the Clauser, Horne, Shimony, and Holt (CHSH) game. By writing the game explicitly as a Bayesian game, the resulting game is modified such the payoff's are different. Crucially, restrictions are imposed on the measurements that Alice and Bob can perform. By imposing these restrictions, it is found that there exists quantum advantage beyond entanglement for a given quantum state. This is shown by decomposing the expected payoff into a classical and quantum term. By optimising over the expected payoff, the classical limit is surpassed for the given state in the restricted measurement space. This gives an operational framework in order to witness and determine the quantum discord for specific states, whilst demonstrating the importance of measurement in quantum advantage.