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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Marriott, C., Watrous, J. Quantum Arthur–Merlin games. comput. complex. 14, 122–152 (2005). https://doi.org/10.1007/s00037-005-0194-x
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DOI: https://doi.org/10.1007/s00037-005-0194-x
Keywords.
- Arthur–Merlin games
- interactive proof systems
- quantum proofs
- quantum complexity theory
- quantum computation