Diagonalization arguments for QMA type proof systems
Yes, diagonalization arguments can still be used. For the oracle separation $\mathcal{QMA}^\mathcal{O}\subsetneq \mathcal{PP}^\mathcal{O}$, design an oracle $\mathcal{O}$ such that the following language separates the classes:

$$L = \{1^n\ |\ \left| \mathcal{O}\cap\{0,1\}^n\right|&gt;\tfrac{1}{2}2^n \}$$

This language is clearly in $\mathcal{PP}^\mathcal{O}$ for any choice of oracle $\mathcal{O}$. However, it is not always in $\mathcal{QMA}^{\mathcal{O}}$, "because" it is difficult for a quantum machine to estimate whether a state $a|0\rangle |\phi\rangle+b|1\rangle |\psi\rangle$ has $|a|&gt;|b|$ when the difference $|a|-|b|=\mathcal{O}(2^{-n})$ is exponentially small. This is true even in the presence of a prover, because even if the prover supplies the correct answer, it is not possible to verify whether the answer is correct. In your terminology: There is no needle to give; rather, the task is to count the number of needles, and then a single needle doesn't help much.

I hope somebody can supply useful literature references.