Is there some (complexity theoretic) argument for or against Quantum-classical Merlin Arthur $$QCMA\subseteq BQP^{NP}?$$
I am aware of one (weak!) supporting argument for posing it as a conjecture. This is due to quantum-classical PCP (QC-PCP) conjecture. If QC-PCP holds then $QCMA\subseteq BQP^{NP}$.
[ Ref: Theorem 1.3 in WFC23 along with their conjecture about QC-PCP (conjecture 6.3). ]
My query: (opinion) I find it a weak supporting argument because there is less unanimity about validity of quantum PCP.
I am looking for some other convincing argument for $QCMA\subseteq BQP^{NP}$.
- I am looking how they behave in the relativised (oracle) world.
- Some implication of assumption $BQP^{NP} \subseteq QCMA$ on (some version) of Quantum polynomial hierarchy. (Assuming robustness of the hierarchy).
