Even quantum advice is unlikely to solve PP

We give a corrected proof that if PP ⊆ BQP/qpoly, then the Counting Hierarchy collapses, as originally claimed by Aaronson CCC'06 arXiv:cs/0504048. This recovers the related unconditional claim that PP does not have circuits of any fixed size nᵏ even with quantum advice. We do so by proving that YQP*, an oblivious version of (QMA ∩ coQMA), is contained in APP, and so is PP-low.