Toward a general theory of quantum games
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-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.
Cite
@article{arxiv.quant-ph/0611234,
title = {Toward a general theory of quantum games},
author = {Gus Gutoski and John Watrous},
journal= {arXiv preprint arXiv:quant-ph/0611234},
year = {2013}
}
Comments
23 pages, 12pt font, single-column compilation of STOC 2007 final version