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computational complexity

, Volume 14, Issue 2, pp 122–152 | Cite as

Quantum Arthur–Merlin games

  • Chris Marriott
  • John Watrous
Open Access
Original Paper

Abstract.

This paper studies quantum Arthur–Merlin games, which are Arthur–Merlin games in which Arthur and Merlin can perform quantum computations and Merlin can send Arthur quantum information. As in the classical case, messages from Arthur to Merlin are restricted to be strings of uniformly generated random bits. It is proved that for one-message quantum Arthur–Merlin games, which correspond to the complexity class QMA, completeness and soundness errors can be reduced exponentially without increasing the length of Merlin’s message. Previous constructions for reducing error required a polynomial increase in the length of Merlin’s message. Applications of this fact include a proof that logarithmic length quantum certificates yield no increase in power over BQP and a simple proof that \( {\text{QMA}} \subseteq {\text{PP}}. \) Other facts that are proved include the equivalence of three (or more) message quantum Arthur–Merlin games with ordinary quantum interactive proof systems and some basic properties concerning two-message quantum Arthur–Merlin games.

Keywords.

Arthur–Merlin games interactive proof systems quantum proofs quantum complexity theory quantum computation 

Subject classification.

68Q10 68Q15 

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • Chris Marriott
    • 1
  • John Watrous
    • 1
  1. 1.Department of Computer ScienceUniversity of CalgaryCalgaryCanada

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