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-Jamiolkowski 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. Categories and Subject Descriptors putation by Abstract Devices]: Modes of Computation, Complexity Measures and Classes General Terms Theory Keywords Quantum game...

• Type: Conference
• Year: 2007
• Where: STOC
• Authors: Gus Gutoski, John Watrous
• Keywords: Algorithms, Classes General Terms, Positive Semidefinite Operator, STOC 2007, Subject Descriptors Putation