Quantum Merlin-Arthur Proof Systems: Are Multiple Merlins More Helpful to Arthur?
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This paper introduces quantum ``multiple-Merlin''-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical single-proof systems (i.e., usual Merlin-Arthur proof systems), it is unclear whether or not quantum multi-proof systems collapse to quantum single-proof systems (i.e., usual quantum Merlin-Arthur proof systems). This paper presents a necessary and sufficient condition under which the number of quantum proofs is reducible to two. It is also proved that, in the case of perfect soundness, using multiple quantum proofs does not increase the power of quantum Merlin-Arthur proof systems.
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Cited by 2 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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Unentangled stoquastic Merlin-Arthur proof systems: 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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