Stoquastic acceptance floor ($p_{+}\ge 1/2$)

If the output of a stoquastic circuit is $|0⟩|r_0⟩+|1⟩|r_1⟩$ with nonnegative amplitudes, its plus-outcome probability is $1/2+\mathrm{Re}⟨r_0|r_1⟩\ge 1/2$. Basis quantum witnesses with zero and plus ancilla qubits always have this property. A soundness threshold below one half cannot hold for every such input.