Investigations in quantum games using EPR - type set - ups by 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. Reproducing the properties of quantum correlation games appears to be conceptually impossible within the framework of classical games. The second approach in the present thesis is based on the fact that all derivations of the Bell inequalities assume local hidden variable (LHV) models which produce a set of positive-definite probabilities for detecting a particle with a given spin orientation. In recent years it has been shown that when the predictions of a 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. Thesis Supervisor: Dr. Timothy Scott Title: Senior Lecturer