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We study a variant of QMA where quantum proofs have no relative phase (i.e.non-negative amplitudes, up to a global phase). If only completeness ismodified, this class is equal to QMA [arXiv:1410.2882]; but if bothcompleteness and soundness are modified, the class (named QMA+ by Jeronimo andWu) can be much more powerful. We show that QMA+ with some constant gap isequal to NEXP, yet QMA+ with some *other* constant gap is equal to QMA. Oneinterpretation is that Merlin's ability to "deceive" originates from relativephase at least as much as from entanglement, since QMA(2) $\subseteq$ NEXP.

Quantum Merlin-Arthur and proofs without relative phase