Playing Games with EPR-Type Experiments

Azhar Iqbal, Azhar Iqbal

Published Jan 1, 2005• 21 citations

Abstract

An approach towards quantum games is proposed that uses the unusual probabilities involved in EPR-type experiments directly in two-player games. Key words: Quantum games; Local hidden variable; Bell-CHSH inequality; negative probability measure.

Related papers

Playing games with EPR-type experiments

Azhar Iqbal

An approach towards quantum games is proposed that uses the unusual probabilities involved in EPR-type experiments directly in two-player games.

arXiv:quant-ph/0507152Journal of Physics A Mathematical and GeneralOct 12, 200515 citations

Investigations in quantum games using EPR-type set-ups

Azhar Iqbal

Research in quantum games has flourished during recent years. However, it seems that opinion remains divided about their true quantum character and content. For example, one argument says that quantum games are nothing but 'disguised' classical games and that to quantize a game is equivalent to replacing the original game by a different classical game. The present thesis contributes towards the ongoing debate about quantum nature of quantum games by developing two approaches addressing the related issues. Both approaches take Einstein-Podolsky-Rosen (EPR)-type experiments as the underlying physical set-ups to play two-player quantum games. In the first approach, the players' strategies are unit vectors in their respective planes, with the knowledge of coordinate axes being shared between them. Players perform measurements in an EPR-type setting and their payoffs are defined as functions of the correlations, i.e. without reference to classical or quantum mechanics. Classical bimatrix games are reproduced if the input states are classical and perfectly anti-correlated, as for a classical correlation game. However, for a quantum correlation game, with an entangled singlet state as input, qualitatively different solutions are obtained. The second approach uses the result that when the predictions of a Local Hidden Variable (LHV) model are made to violate the Bell inequalities the result is that some probability measures assume negative values. With the requirement that classical games result when the predictions of a LHV model do not violate the Bell inequalities, our analysis looks at the impact which the emergence of negative probabilities has on the solutions of two-player games which are physically implemented using the EPR-type experiments.

arXiv:quant-ph/0604188Apr 25, 20061 citation

Probabilistic analysis of three-player symmetric quantum games played using EPR setting

Azhar Iqbal, Taksu Cheon, Derek Abbott

Apr 15, 20080 citations

Classical rules in quantum games

S. J. van Enk, R. Pike

We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.

arXiv:quant-ph/0203133Physical Review AAug 6, 2002125 citations

Two-player quantum games: When player strategies are via directional choices

Azhar Iqbal, Derek Abbott

Abstract We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player’s spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players’ choices to specific spatial trajectories. We show that for players’ directional choices for which the Bell-CHSH inequality is violated, the players’ payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.

arXiv:2107.01256Quantum Information ProcessingJun 1, 20223 citations

On the Implication of Bell's Probability Distribution and Proposed Experiments of Quantum Measurement

Hai-Long Zhao

In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the distribution of the joint measurement outcomes on the two sides. So it is a function of both hidden variable and settings. In this case, Bell's inequalities fail. Our further analysis shows that Bell's locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, thus violation of Bell's inequalities cannot rule out the existence of local hidden variable. In order to explain the results of EPR-type experiments, we suppose that polarization entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any non-local influence on it. Then several experiments are suggested to reveal the components of polarization entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with a same quantum state will behave in the same way under the same measuring condition.

Jun 1, 20090 citations