MA ⊆ QCMA

Inclusion · quantum setting · folklore

Statement

$\mathbf{MA}\subseteq \mathbf{QCMA}$: every Merlin–Arthur proof system is a QCMA proof system whose verifier computes classically, with the same classical witnesses, completeness and soundness — folklore.

Sketch

The quantum verifier runs the classical verification circuit, drawing Arthur’s coins by measuring qubits prepared in the uniform superposition, so every acceptance probability is preserved exactly.