QMA/qpoly /spl sube/ PSPACE/poly: de-Merlinizing quantum protocols

Abstract

This paper introduces a new technique for removing existential quantifiers over quantum states. Using this technique, 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 sube PP/poly, and offers an intriguing counterpoint to the recent discovery of Raz that QIP/qpoly = ALL. Finally, we show that QCMA/qpoly sube PP/poly and that QMA/rpoly = QMA/poly