On perfect completeness for QMA
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Whether the class QMA (Quantum Merlin Arthur) is equal to QMA1, or QMA with onesided error, has been an open problem for years. This note helps to explain why the problem is difficult, by using ideas from real analysis to give a "quantum oracle" relative to which QMA ≠ QMA1. As a byproduct, we find that there are facts about quantum complexity classes that are classically relativizing but not quantumly relativizing, among them such "trivial" containments as BQP ⊆ ZQEXP.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Quantum Information & Computation
Association for Computing Machinery (ACM)
Aaronson, Scott. "On perfect completeness for QMA." Quantum Information & Computation 9:1 (January 2009), pp. 81-89.
Author's final manuscript