  We study three variants of multi-prover quantum Merlin-Arthur proof systems.
We first show that the class of problems that can be efficiently verified using
polynomially many quantum proofs, each of logarithmic-size, is exactly MQA
(also known as QCMA), the class of problems which can be efficiently verified
via a classical proof and a quantum verifier. We then study the class
BellQMA(poly), characterized by a verifier who first applies unentangled,
nonadaptive measurements to each of the polynomially many proofs, followed by
an arbitrary but efficient quantum verification circuit on the resulting
measurement outcomes. We show that if the number of outcomes per nonadaptive
measurement is a polynomially-bounded function, then the expressive power of
the proof system is exactly QMA. Finally, we study a class equivalent to
QMA(m), denoted SepQMA(m), where the verifier's measurement operator
corresponding to outcome "accept" is a fully separable operator across the m
quantum proofs. Using cone programming duality, we give an alternate proof of a
result of Harrow and Montanaro [FOCS, pp. 633--642 (2010)] that shows a perfect
parallel repetition theorem for SepQMA(m) for any m.
