THE ROLE OF CORRELATION IN QUANTUM AND CLASSICAL GAMES

THE ROLE OF CORRELATION IN QUANTUM AND CLASSICAL GAMES We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these simple quantum games are not sensitive to the quantum part of the correlation. In these games played with quantum objects it is possible to transform a game such as Prisoner's Dilemma into the game of Chicken. We show that this behavior, and the associated enhanced equilibrium payoff over playing the game with quantum objects in nonentangled states, is entirely due to the classical part of the correlation.Generalizing these games to the pure strategy 2-player quantum game where the players have finite strategy sets and a projective joint measurement is made on the output state produced by the players, we show that a given quantum game of this form can always be reproduced by a classical model, such as a communication channel. Where entanglement is a feature of the these 2-player quantum games the matrix of expected outcomes for the players can be reproduced by a classical channel with correlated noise. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Fluctuation and Noise Letters: An Interdisciplinary Scientific Journal on Random Processes in Physical, Biological and Technological Systems World Scientific Publishing Company

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Publisher
World Scientific Publishing Company
Copyright
Copyright ©
ISSN
0219-4775
eISSN
1793-6780
D.O.I.
10.1142/S0219477513500119
Publisher site
See Article on Publisher Site

Abstract

We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these simple quantum games are not sensitive to the quantum part of the correlation. In these games played with quantum objects it is possible to transform a game such as Prisoner's Dilemma into the game of Chicken. We show that this behavior, and the associated enhanced equilibrium payoff over playing the game with quantum objects in nonentangled states, is entirely due to the classical part of the correlation.Generalizing these games to the pure strategy 2-player quantum game where the players have finite strategy sets and a projective joint measurement is made on the output state produced by the players, we show that a given quantum game of this form can always be reproduced by a classical model, such as a communication channel. Where entanglement is a feature of the these 2-player quantum games the matrix of expected outcomes for the players can be reproduced by a classical channel with correlated noise.

Journal

Fluctuation and Noise Letters: An Interdisciplinary Scientific Journal on Random Processes in Physical, Biological and Technological SystemsWorld Scientific Publishing Company

Published: Sep 26, 2013

Keywords: Quantum game theory quantum correlation

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