Toward a general theory of quantum games

  • Authors:
  • Gus Gutoski;John Watrous

  • Affiliations:
  • University of Waterloo, Waterloo, ON, Canada;University of Waterloo, Waterloo, ON, Canada

  • Venue:
  • Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
  • Year:
  • 2007

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Abstract

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-Jamiolkowski representation of quantum , with respect to which each strategy is described by a single 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.