QCMA ⊆ QMA

Inclusion · quantum setting · folklore

Statement

$\mathbf{QCMA}\subseteq \mathbf{QMA}$: every QCMA proof system becomes a QMA proof system when the verifier first measures the witness register in the computational basis — folklore.

Sketch

The honest classical witness is sent as a computational-basis state, so completeness is unchanged. Measuring any quantum witness yields a distribution over classical strings, and the acceptance probability is the average of the QCMA verifier’s acceptance probabilities over it, hence at most $1/3$ on no-instances.