Summary: QMA/qpoly PSPACE/poly: De-Merlinizing Quantum Protocols
University of Waterloo
This paper introduces a new technique for removing ex-
istential quantifiers over quantum states. Using this tech-
nique, we show that there is no way to pack an exponential
number of bits into a polynomial-size quantum state, in such
a way that the value of any one of those bits can later be
proven with the help of a polynomial-size quantum witness.
We also show that any problem in QMA with polynomial-
size quantum advice, is also in PSPACE with polynomial-
size classical advice. This builds on our earlier result that
BQP/qpoly PP/poly, and offers an intriguing counter-
point to the recent discovery of Raz that QIP/qpoly = ALL.
Finally, we show that QCMA/qpoly PP/poly and that
QMA/rpoly = QMA/poly.
Let Bob be a graduate student, and let x be an n-bit string
representing his thesis problem. Bob's goal is to learn