In this thesis we introduce quantum refereed games, which are quantum interactive proof systems with two competing provers. We focus on a restriction of this model that we call short quantum games and we prove an upper bound and a lower bound on the expressive power of these games. For the lower bound, we prove that every language having an ordinary quantum interactive proof system also has a short quantum game. An important part of this proof is the establishment of a quantum measurement that reliably distinguishes between quantum states chosen from disjoint convex sets. For the upper bound, we show that certain types of quantum refereed games, including short quantum games, are decidable in deterministic exponential time by supplying a separation oracle for use with the ellipsoid method for convex feasibility.
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