We propose and experimentally demonstrate a zero-sum game that is in a fair Nash equilibrium for classical players, but has the property that a quantum player can always win using an appropriate strategy. The gain of the quantum player is measured experimentally for different quantum strategies and input states. It is found that the quantum gain is maximized by a maximally entangled state, but does not decrease to zero when entanglement disappears. Instead, it links with another kind of quantum correlation described by discord for the qubit case and the connection is demonstrated both theoretically and experimentally.
We propose and experimentally demonstrate a zero-sum game that is in a fair Nash equilibrium for classical players, but has the property that a quantum player can always win using an appropriate strategy. The gain of the quantum player is measured experimentally for different quantum strategies and input states. It is found that the quantum gain is maximized by a maximally entangled state, but does not decrease to zero when entanglement disappears. Instead, it links with another kind of quantum correlation described by discord for the qubit case and the connection is demonstrated both theoretically and experimentally.
We propose and experimentally demonstrate a zero-sum game that is in a fair Nash equilibrium for classical players, but has the property that a quantum player can always win using an appropriate strategy. The gain of the quantum player is measured experimentally for different quantum strategies and input states. It is found that the quantum gain is maximized by a maximally entangled state, but does not decrease to zero when entanglement disappears. Instead, it links with another kind of quantum correlation described by discord for the qubit case and the connection is demonstrated both theoretically and experimentally.
The Nash equilibrium plays a crucial role in game theory. Most of results are based on classical resources. Our goal in this paper is to explore multipartite zero-sum game with quantum settings. We find that in two different settings there is no strategy for a tripartite classical game being fair. Interestingly, this is resolved by providing dynamic zero-sum quantum games using single quantum state. Moreover, the gains of some players may be changed dynamically in terms of the committed state. Both quantum games are robust against the preparation noise and measurement errors.
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.
Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of novel game strategies that lead to new (quantum Nash) equilibrium points whereby players in some classical games are always outperformed if sharing and processing joint information ruled by the laws of quantum physics is allowed. We show that, for a bipartite non zero-sum game, input local quantum correlations, and separable states in particular, suffice to achieve an advantage over any strategy that uses classical resources, thus dispensing with quantum nonlocality, entanglement, or even discord between the players' input states. This highlights the remarkable key role played by pure quantum coherence at powering some protocols. Finally, we propose an experiment that uses separable states and basic photon interferometry to demonstrate the locally-correlated quantum advantage.
A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of correlations , i.e. without reference to classical or quantum mechanics. Classical bi-matrix games are reproduced if the input states are classical and perfectly anti-correlated, that is, for a classical correlation game. However, for a quantum correlation game, with an entangled singlet state as input, qualitatively different solutions are obtained. For example, the Prisoners' Dilemma acquires a Nash equilibrium if both players apply a mixed strategy. It appears to be conceptually impossible to reproduce the properties of quantum correlation games within the framework of classical games.
A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of correlations, i.e. without reference to classical or quantum mechanics. Classical bi-matrix games are reproduced if the input states are classical and perfectly anti-correlated, that is, for a classical correlation game. However, for a quantum correlation game, with an entangled singlet state as input, qualitatively different solutions are obtained. For example, the Prisoners' Dilemma acquires a Nash equilibrium if both players apply a mixed strategy. It appears to be conceptually impossible to reproduce the properties of quantum correlation games within the framework of classical games.