Superposition detection and QMA with non-collapsing measurements

Abstract

We prove that $\sf{QMA}$ where the verifier may also make a single $non-collapsing$ measurement [7] is equal to $\sf{NEXP}$, resolving an open question of Aaronson [5]. We show this is a corollary to a modified proof of $\sf{QMA+ = NEXP}$ [15]. At the core of many results inspired by Blier and Tapp [16] is an unphysical property testing problem deciding whether a quantum state is close to an element of a fixed basis.