QMA/qpoly Is Contained In 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 is contained in PP/poly, and offers an intriguing counterpoint to the recent discovery of Raz that QIP/qpoly = ALL. Finally, we show that QCMA/qpoly is contained in PP/poly and that QMA/rpoly = QMA/poly.
Cite
@article{arxiv.quant-ph/0510230,
title = {QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum Protocols},
author = {Scott Aaronson},
journal= {arXiv preprint arXiv:quant-ph/0510230},
year = {2007}
}
Comments
13 pages. Final version to appear in Complexity 2006; fills in some gaps in the proofs