Quantum Arthur-Merlin Games
Chris Marriott, John Watrous

TL;DR
This paper explores quantum Arthur-Merlin games, demonstrating error reduction techniques, equivalences with quantum interactive proofs, and implications for quantum complexity classes like QMA, BQP, and PP.
Contribution
It introduces exponential error reduction for one-message quantum Arthur-Merlin games and establishes their equivalence with quantum interactive proof systems.
Findings
Exponential error reduction in QMA without increasing message length
Logarithmic quantum certificates do not surpass BQP
QMA is contained within PP
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 QMA is contained in PP. Other facts that are proved include the equivalence of three (or more) message quantum…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Cryptography and Data Security · Quantum Information and Cryptography
