1 research outputs found
Investigations in quantum games using EPR-type set-ups
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.Comment: PhD thesis, University of Hull, 2006, 10 figures, 114 pages, defended
on Feb 14, 2006. The official version of this thesis is available from the
University of Hull, U