Separating pseudo-telepathy games and two-local theories

We give an $\dfrac{1}{54}$ separation between 5-party pseudo-telepathy games and two-local theories. We define the notion of strategy in a k-local theory for a game, and extend the method of Chao and Reichardt. We also study variation of the game to minimize the classical winning probability

How Quantum Information can improve Social Welfare

It has been shown elsewhere that quantum resources can allow us to achieve a family of equilibria that can have sometimes a better social welfare, while guaranteeing privacy. We use graph games to propose a way to build non-cooperative games from graph states, and we show how to achieve an unlimited improvement with quantum advice compared to classical advice

Improving social welfare in non-cooperative games with different types of quantum resources

We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can improve social welfare, a measure of the quality of a Nash equilibrium. We study how these advantages in quantum social welfare depend on the bias of the game, and improve upon the separation that was previously obtained using pseudo-telepathic strategies. Two different quantum settings are analysed: a first, in which players are given direct access to an entangled quantum state, and a second, which we introduce here, in which they are only given classical advice obtained from quantum devices. For a given game G, these two settings give rise to different equilibria characterised by the sets of equilibrium correlations Qcorr(G) and Q(G), respectively. We show that Q(G) ⊆ Qcorr(G) and, by considering explicit example games and exploiting SDP optimisation methods, provide indications of a strict separation between the social welfare attainable in the two settings. This provides a new angle towards understanding the limits and advantages of delegating quantum measurements

Noisy three-player dilemma game: Robustness of the quantum advantage

Games involving quantum strategies often yield higher payoff. Here, we study a practical realization of the three-player dilemma game using the superconductivity-based quantum processors provided by IBM Q Experience. We analyze the persistence of the quantum advantage under corruption of the input states and how this depends on parameters of the payoff table. Specifically, experimental fidelity and error are observed not to be properly anti correlated, i.e., there are instances where a class of experiments with higher fidelity yields a greater error in the payoff. Further, we find that the classical strategy will always outperform the quantum strategy if corruption is higher than half.Comment: Persistence of the quantum advantage under corruption of the input states is analyzed for a 3-player dilemma game implemented using superconductivity-based quantum processor

Quantum magic rectangles: Characterization and application to certified randomness expansion

We study a generalization of the Mermin-Peres magic square game to arbitrary rectangular dimensions. After exhibiting some general properties, these rectangular games are fully characterized in terms of their optimal win probabilities for quantum strategies. We find that for $m \times n$ rectangular games of dimensions $m,n \geq 3$ there are quantum strategies that win with certainty, while for dimensions $1 \times n$ quantum strategies do not outperform classical strategies. The final case of dimensions $2 \times n$ is richer, and we give upper and lower bounds that both outperform the classical strategies. Finally, we apply our findings to quantum certified randomness expansion to find the noise tolerance and rates for all magic rectangle games. To do this, we use our previous results to obtain the winning probability of games with a distinguished input for which the devices give a deterministic outcome, and follow the analysis of C. A. Miller and Y. Shi [SIAM J. Comput. 46, 1304 (2017)].Comment: 23 pages, 3 figures; published version with minor correction

Improving social welfare in non-cooperative games with different types of quantum resources

We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can lead to new Nash equilibria and improve social welfare — a measure of the quality of an equilibrium. Two different quantum settings are analysed: a first, in which players are given direct access to an entangled quantum state, and a second, which we introduce here, in which they are only given classical advice obtained from quantum devices. For a given game $G$, these two settings give rise to different equilibria characterised by the sets of equilibrium correlations $Q_\textrm{corr}(G)$ and $Q(G)$, respectively. We show that $Q(G)\subseteq Q_\textrm{corr}(G)$, and by exploiting the self-testing property of some correlations, that the inclusion is strict for some games $G$. We make use of SDP optimisation techniques to study how these quantum resources can improve social welfare, obtaining upper and lower bounds on the social welfare reachable in each setting. We investigate, for several games involving conflicting interests, how the social welfare depends on the bias of the game and improve upon a separation that was previously obtained using pseudo-telepathic solutions

Bell nonlocality

Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem has been a central theme of research from a variety of perspectives, mainly motivated by quantum information science, where the nonlocality of quantum theory underpins many of the advantages afforded by a quantum processing of information. The focus of this review is to a large extent oriented by these later developments. We review the main concepts and tools which have been developed to describe and study the nonlocality of quantum theory, and which have raised this topic to the status of a full sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio