Connection between Bell nonlocality and Bayesian game theory

Brunner, Nicolás; Linden, Noah

doi:10.1038/ncomms3057

Cited by 119 publications

(137 citation statements)

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“…Recently, Brunner and Linden made the connection between Bell test scenarios and games with incomplete information more explicit and provided examples of such games where quantum mechanics offers an advantage [6]. A game with incomplete information (or Bayesian game) is a game where the two parties receive some input unknown to the other party [7].…”

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confidence: 99%

“…Moreover, both players equally prefer each of the equilibria, hence there is no conflict on which one to choose. Another example is the CHSH game, where we can assume that both Alice and Bob win 1 point if the parity of their outputs is equal to the logical AND of their inputs, and they lose 1 point otherwise (see Example 1 in [6]). In fact, other known nonlocal games, including the GHZ-Mermin game [10], the Magic Square Game [11,12], the Hidden Matching game [13,14], Brunner and Linden's three games [6], are all examples of common interest games [25].…”

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Nonlocality and Conflicting Interest Games

et al. 2015

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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. Nonlocality is one of the most important and elusive properties of quantum mechanics, where two spatially separated observers sharing a pair of entangled quantum bits can create correlations that cannot be explained by any local realistic theory. More precisely, Bell [1] showed that there exist scenarios where correlations between any local hidden variables can be shown to satisfy specific constraints (known as Bell inequalities), while these constraints can nevertheless be violated by correlations created by quantum systems.An equivalent way of describing Bell test scenarios is in the language of nonlocal games. The best-known example is the CHSH game [2]: Alice and Bob, who are spatially separated and cannot communicate, receive an input bit x and y respectively and must output bits a and b respectively, such that the outputs are different if both input bits are equal to 1, and the same otherwise. It is well known that the probability over uniform inputs that they jointly win this game when they a priori share classical resources is 0.75, while if they share and appropriately measure a pair of maximally entangled qubits, they can jointly win the game with probability cos 2 π/8 > 0.75. The classical value 0.75 corresponds to the upper bound of a Bell inequality and the CHSH game provides an example of a Bell inequality violation, since there exist quantum strategies that violate this bound.Looking at Bell inequalities through the lens of games has been very useful in practice, including in cryptography [3,4] and quantum information [5], where, for example, quantum mechanics offers stronger than classical security guarantees in quantum key distribution or verification protocols. Recently, Brunner and Linden made the connection between Bell test scenarios and games with incomplete information more explicit and provided examples of such games where quantum mechanics offers an advantage [6]. A game with incomplete information (or Bayesian game) is a game where the two parties receive some input unknown to the other party [7]. We remark that without more restrictions, quantum mechanics only offers advantages for incomplete information games, i.e., when the parties receive inputs or, in other word...

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Nonlocality and Conflicting Interest Games

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“…(ii) For ǫ = 0, all the games G(ǫ) are asymmetric and Bob has some advantage over Alice. (Such situations can occur, for instance, in example 3 of the game discussed in [13], when the two competing companies A and B can be of different size. )…”

Section: Class Of Two Party Bayesian Gamesmentioning

confidence: 99%

“…An interesting connection between Bell nonlocality [5] (which can be realized in quantum mechanics through entangled states) and Bayesian games introduced by Harsanyi [14] was established in [13]. Soon after, an explicit example of a two-party game with conflicting interests where an entangled state leads to a better solution was provided in [9] and has inspired a number of interesting works along this direction [10,11,[15][16][17][18][19].…”

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Strong quantum solutions in conflicting-interest Bayesian games

Rai

Paul

2017

Phys. Rev. A

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Quantum entanglement has been recently demonstrated as a useful resource in conflicting interest games of incomplete information between two players, Alice and Bob [Pappa et al., Phys. Rev. Lett. 114, 020401 (2015)]. General setting for such games is that of correlated strategies where the correlation between competing players is established through a trusted common adviser; however, players need not reveal their input to the adviser. So far, quantum advantage in such games has been revealed in a restricted sense. Given a quantum correlated equilibrium strategy, one of the players can still receive a higher than quantum average payoff with some classically-correlated equilibrium strategy. In this work, by considering a class of asymmetric Bayesian games, we show the existence of games with quantum correlated equilibrium where average payoff of both the players exceed respective individual maximum for each player over all classically-correlated equilibriums.

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Can Biological Quantum Networks Solve NP‐Hard Problems?

Wendin

2019

Adv Quantum Tech

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There is a widespread view that the human brain is so complex that it cannot be efficiently simulated by universal Turing machines, let alone ordinary classical computers. During the last decades the question has therefore been raised whether it is needed to consider quantum effects to explain the imagined cognitive power of a conscious mind. Not surprisingly, the conclusion is that quantum‐enhanced cognition and intelligence are very unlikely to be found in biological brains. Quantum effects may certainly influence signaling pathways at the molecular level in the brain network, like ion ports, synapses, sensors, and enzymes. This might evidently influence the functionality of some nodes and perhaps even the overall intelligence of the brain network, but hardly give it any dramatically enhanced functionality. The conclusion is that biological quantum networks can only approximately solve small instances of nonpolynomial (NP)‐hard problems. On the other hand, artificial intelligence and machine learning implemented in complex dynamical systems based on genuine quantum networks can certainly be expected to show enhanced performance and quantum advantage compared with classical networks. Nevertheless, even quantum networks can only be expected to solve NP‐hard problems approximately. In the end it is a question of precision—Nature is approximate.

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Connection between Bell nonlocality and Bayesian game theory

Cited by 119 publications

References 32 publications

Nonlocality and Conflicting Interest Games

Nonlocality and Conflicting Interest Games

Strong quantum solutions in conflicting-interest Bayesian games

Can Biological Quantum Networks Solve NP‐Hard Problems?

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