We develop a method for the transfer of perfect strategies between various classes of two-player, one round cooperative non-local games with quantum inputs and outputs using the simulation paradigm in quantum information theory. We show that such a transfer is possible when canonically associated operator spaces for each game are quantum homomorphic or isomorphic, as defined in [21]. We examine a new class of QNS correlations, needed for the transfer of strategies between games, and characterize them in terms of states on tensor products of canonical operator systems. We define jointly tracial correlations and show they correspond to traces acting on tensor products of canonical C*-algebras associated with individual game parties. We then make an inquiry into the initial application of such results to the study of concurrent quantum games.

I would like to thank my advisor Ivan G. Todorov for the many fruitful discussions on earlier drafts of the paper. I would also like to thank Lyudmila Turowska for helpful comments on some results in the last section, and Alexandros Chatzinikolaou for identifying the gap in the proof of [20, Lemma 5.8], necessitating the change in definition. Finally, I would like to thank the referee(s) for their detailed reading and remarks.