Toward a general theory of quantum games
<|reference_start|>Toward a general theory of quantum games: We study properties of quantum strategies, which are complete specifications of a given party's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantum strategies that generalizes the Choi-Jamio{\l}kowski representation of quantum operations. This new representation associates with each strategy a positive semidefinite operator acting only on the tensor product of its input and output spaces. Various facts about such representations are established, and two applications are discussed: the first is a new and conceptually simple proof of Kitaev's lower bound for strong coin-flipping, and the second is a proof of the exact characterization QRG = EXP of the class of problems having quantum refereed games.<|reference_end|>
@article{gutoski2006toward,
    title={Toward a general theory of quantum games},
    author={Gus Gutoski and John Watrous},
    journal={Proceedings of STOC 2007, pages 565-574},
    year={2006},
    doi={10.1145/1250790.1250873},
    archivePrefix={arXiv},
    eprint={quant-ph/0611234},
    primaryClass={quant-ph cs.CC cs.GT}
}