Short Quantum Games

TL;DR

This thesis introduces short quantum games, a restricted form of quantum interactive proof systems with two competing provers, establishing their expressive power and decidability within exponential time.

Contribution

It proves that all languages with quantum interactive proofs can be represented as short quantum games and shows their decidability using convex optimization techniques.

Findings

Short quantum games can simulate all quantum interactive proof systems.

Decidability of certain quantum refereed games in exponential time.

Quantum measurements can distinguish states from disjoint convex sets.

Abstract

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.