Today I read a paper titled “Toward a general theory of quantum games”
The abstract is:
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.