Quantum game players can have advantage without discord

TL;DR

This paper demonstrates that in a specific quantum game, players can gain a quantum advantage without the presence of discord, challenging the traditional view that discord is necessary for quantum advantage.

Contribution

It introduces a zero-sum game where quantum advantage arises from correlations lacking discord, prompting a reevaluation of discord's role in quantum advantage.

Findings

Quantum advantage exists without discord in a specific game scenario.

Classical equilibrium can be fair yet still allow quantum players to outperform.

Discord is not a necessary condition for quantum advantage in all game-theoretic contexts.

Abstract

The last two decades have witnessed a rapid development of quantum information processing, a new paradigm which studies the power and limit of "quantum advantages" in various information processing tasks. Problems such as when quantum advantage exists, and if existing, how much it could be, are at a central position of these studies. In a broad class of scenarios, there are, implicitly or explicitly, at least two parties involved, who share a state, and the correlation in this shared state is the key factor to the efficiency under concern. In these scenarios, the shared \emph{entanglement} or \emph{discord} is usually what accounts for quantum advantage. In this paper, we examine a fundamental problem of this nature from the perspective of game theory, a branch of applied mathematics studying selfish behaviors of two or more players. We exhibit a natural zero-sum game, in which the chance for any player to win the game depends only on the ending correlation. We show that in a certain classical equilibrium, a situation in which no player can further increase her payoff by any local classical operation, whoever first uses a quantum computer has a big advantage over its classical opponent. The equilibrium is fair to both players and, as a shared correlation, it does not contain any discord, yet a quantum advantage still exists. This indicates that at least in game theory, the previous notion of discord as a measure of non-classical correlation needs to be reexamined, when there are two players with different objectives.