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Register a new userQuantum advice enhances social optimality in three-party conflicting interest games
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Quantum pseudo-telepathy games are good examples of explaining the strangeness of quantum mechanics and demonstrating the advantage of quantum resources over classical resources. Most of the quantum pseudo-telepathy games are common interest games, nevertheless conflicting interest games are more widely used to model real world situations. Recently Pappa et al. (Phys. Rev. Lett. 114, 020401, 2015) proposed the first two-party conflicting interest game where quantum advice enhances social optimality. In the present paper we give two new three-party conflicting interest games and show that quantum advice can enhance social optimality in a three-party setting. The first game we propose is based on the famous GHZ game which is a common interest game. The second game we propose is related to the Svetlichny inequality which demonstrates quantum mechanics cannot be explained by the local hidden variable model in a three-party setting.
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A significant aspect of the study of quantum strategies is the exploration of the game-theoretic solution concept of the Nash equilibrium in relation to the quantization of a game. Pareto optimality is a refinement on the set of Nash equilibria. A refinement on the set of Pareto optimal outcomes is known as social optimality in which the sum of players payoffs are maximized. This paper analyzes social optimality in a Bayesian game that uses the setting of generalized Einstein-Podolsky-Rosen experiments for its physical implementation. We show that for the quantum Bayesian game a direct connection appears between the violation of Bells inequality and the social optimal outcome of the game and that it attains a superior socially optimal outcome.
Nonlocality, one of the most remarkable aspects of quantum mechanics, is closely related to Bayesian game theory. Quantum mechanics can offer advantages to some Bayesian games, if the payoff functions are related to Bell inequalities in some way. Most of these Bayesian games that have been discussed are common interest games. Recently the first conflicting interest Bayesian game is proposed in Phys. Rev. Lett. 114, 020401 (2015). In the present paper we present three new conflicting interest Bayesian games where quantum mechanics offers advantages. The first game is linked with Cereceda inequalities, the second game is linked with a generalized Bell inequality with 3 possible measurement outcomes, and the third game is linked with a generalized Bell inequality with 3 possible measurement settings.
With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as a prospective method to generate three party quantum networks which can be further used to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in the situations wherever the availability of entangled pairs is limited. In addition to that we focus on the problem of distinguishing networks created by cloning from those which are created by distributing independently generated entangled pairs. We find that there are several states which cannot be distinguished using the Finner inequalities in the standard way. For such states, we propose an extension to the existing Finner inequality for triangle networks by further increasing the number of observers from three to four or six depending on the network topology. This takes into account the additional correlations that exist in the case of cloned networks. In the last part of the article we have used tripartite mutual information to distinguish cloned networks from networks created by independent sources and have further used squashed entanglement as a measure to quantify the amount of dependence in the cloned networks.
We develop a three-party quantum secret sharing protocol based on arbitrary dimensional quantum states. In contrast to the previous quantum secret sharing protocols, the sender can always control the state, just using local operations, for adjusting the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.
We consider the problem of decorrelating states of coupled quantum systems. The decorrelation can be seen as separation of quantum signals, in analogy to the classical problem of signal-separation rising in the so-called cocktail-party context. The separation of signals cannot be achieved perfectly, and we analyse the optimal decorrelation map in terms of added noise in the local separated states. Analytical results can be obtained both in the case of two-level quantum systems and for Gaussian states of harmonic oscillators.
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