 
Summary: The Power of Unentanglement
Scott Aaronson
MIT
Salman Beigi
MIT
Andrew Drucker
MIT
Bill Fefferman
University of Chicago
Peter Shor
MIT
Abstract
The class QMA (k), introduced by Kobayashi et al., consists of all languages that can be
verified using k unentangled quantum proofs. Many of the simplest questions about this class
have remained embarrassingly open: for example, can we give any evidence that k quantum
proofs are more powerful than one? Does QMA (k) = QMA (2) for k 2? Can QMA (k)
protocols be amplified to exponentially small error?
In this paper, we make progress on all of the above questions.
· We give a protocol by which a verifier can be convinced that a 3Sat formula of size m is
satisfiable, with constant soundness, given O (
