  This paper presents stronger methods of achieving perfect completeness in
quantum interactive proofs. First, it is proved that any problem in QMA has a
two-message quantum interactive proof system of perfect completeness with
constant soundness error, where the verifier has only to send a constant number
of halves of EPR pairs. This in particular implies that the class QMA is
necessarily included by the class QIP_1(2) of problems having two-message
quantum interactive proofs of perfect completeness, which gives the first
nontrivial upper bound for QMA in terms of quantum interactive proofs. It is
also proved that any problem having an $m$-message quantum interactive proof
system necessarily has an $(m+1)$-message quantum interactive proof system of
perfect completeness. This improves the previous result due to Kitaev and
Watrous, where the resulting system of perfect completeness requires $m+2$
messages if not using the parallelization result.
