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Quantum Information Processing

Experimental demonstration of conflicting interest nonlocal games using superconducting qubits

Haozhen Situ, Lvzhou Li, Zhiming Huang, Zhimin He, Cai Zhang

Published Apr 18, 2018• 0 citations
Publisher
DOI
10.1007/s11128-018-1895-9

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Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform the best classical strategies in common interest Bayesian games and can also surpass the fair classical equilibrium payoffs in conflicting games. However a conflicting game may have unfair equilibrium strategies, which are the archetypal of such games and never occur in common interest games. In this work, making the connection between nonlocality and Bayesian game more striking, we show that quantum strategies can outperform even the unfair classical equilibrium strategies in conflicting games. For this purpose here we consider the conflicting game proposed in [Phys. Rev. Lett. 114, 020401 (2015)]. Moreover, we provide a complete characterization of the nonlocal correlations that are advantageous over the best fair and unfair classical strategies in the said game.
Nonlocality enables two parties to win specific games with probabilities strictly higher than allowed by any classical theory. Nevertheless, all known such examples consider games where the two parties have a common interest, since they jointly win or lose the game. The main question we ask here is whether the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We answer this in the affirmative by presenting a simple conflicting interest game, where quantum strategies outperform classical ones. Moreover, we show that our game has a fair quantum equilibrium with higher payoffs for both players than in any fair classical equilibrium. Finally, we play the game using a commercial entangled photon source and demonstrate experimentally the quantum advantage.
We outline the general construction of three-player games with incomplete information which fulfil the following conditions: (i) symmetry with respect to the permutations of players; (ii) the existence of an upper bound for total payoff resulting from Bell inequalities; (iii) the existence of both fair and unfair Nash equilibria saturating this bound. Conditions (i)–(iii) imply that we are dealing with conflicting interest games. An explicit example of such a game is given. A quantum counterpart of this game is considered. It is obtained by keeping the same utilities but replacing classical advisor by a quantum one. It is shown that the quantum game possesses only fair equilibria with strictly higher payoffs than in the classical case. This implies that quantum nonlocality can be used to resolve the conflict between the players.