Superposition detection and QMA with non-collapsing measurements

We prove that QMA where the verifier may also make a single non-collapsing measurement is equal to NEXP, resolving an open question of Aaronson. We show this is a corollary to a modified proof of QMA+ = NEXP arXiv:2306.13247. At the core of many results inspired by Blier and Tapp arXiv:0709.0738 is an unphysical property testing problem deciding whether a quantum state is close to an element of a fixed basis.