  We define and study a variant of QMA (Quantum Merlin Arthur) in which Arthur
can make multiple non-collapsing measurements to Merlin's witness state, in
addition to ordinary collapsing measurements. By analogy to the class PDQP
defined by Aaronson, Bouland, Fitzsimons, and Lee (2014), we call this class
PDQMA. Our main result is that PDQMA = NEXP; this result builds on the MIP =
NEXP Theorem and complements the result of Aaronson (2018) that PDQP/qpoly =
ALL. While the result has little to do with quantum mechanics, we also show a
more "quantum" result: namely, that QMA with the ability to inspect the entire
history of a hidden variable is equal to NEXP, under mild assumptions on the
hidden-variable theory. We also observe that a quantum computer, augmented with
quantum advice and the ability to inspect the history of a hidden variable, can
solve any decision problem in polynomial time.
