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Quantum Arthur-Merlin Games
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Quantum Arthur-Merlin Games
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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 Arthur-Merlin games with ordinary quantum interactive proof systems and some basic properties concerning two-message quantum Arthur-Merlin games.
Forward citations
Cited by 4 Pith papers
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The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems
StoqMa(k) equals StoqMa for any polynomial k via a positive value-based de Finetti theorem that approximates nonnegative product values with symmetric extensions.
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The power of unentanglement without destructive interference
StoqMA(2) contains NP via Õ(√n)-qubit unentangled stoquastic proofs (nearly perfect completeness) and is contained in EXP, with ETH-optimal parameters matching a refined BKS Sum-of-Squares bound.
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The power of unentanglement without destructive interference
StoqMA(2) contains NP with Õ(√n)-qubit proofs and completeness error 2^{-polylog(n)}, is contained in EXP, and satisfies StoqMA(k)=StoqMA(2) for k≥2 when completeness error is negligible.
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A slightly improved upper bound for quantum statistical zero-knowledge
QSZK and its non-interactive variant NIQSZK stay inside QIP(2)∩co-QIP(2), now with an honest prover that runs in quantum linear space and single-exponential time.
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