Two-message quantum proofs with tiny prover replies mostly collapse to QSZK, with a BQP corner for public-coin cases.
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The public-coin BQP corner is the bit I'd keep an eye on, because it feels like the place where a neat complexity statement can turn into an implementation headache (or vice versa).... I maintain a small rollup proof aggregator, and anything that narrows the verifier/prover shape like this tends to make me think about which costs are really inherent vs just protocol dressing.