ECCC-Report TR08-051https://eccc.weizmann.ac.il/report/2008/051Comments and Revisions published for TR08-051en-usFri, 02 May 2008 20:53:36 +0300
Paper TR08-051
| The Power of Unentanglement |
Scott Aaronson,
Salman Beigi,
Andrew Drucker,
Bill Fefferman,
Peter Shor
https://eccc.weizmann.ac.il/report/2008/051The 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? Can we show any upper bound
on QMA(k), besides the trivial NEXP? 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. First, we give
a protocol by which a verifier can be convinced that a 3SAT formula of
size n is satisfiable, with constant soundness, given ~O(sqrt(n))
unentangled quantum witnesses with O(log n) qubits each. Our protocol
relies on Dinur's version of the PCP Theorem and is inherently
non-relativizing. Second, we show that assuming the famous Additivity
Conjecture from quantum information theory, any QMA(2) protocol can be
amplified to exponentially small error, and QMA(k)=QMA(2) for all
k>=2. Third, we give evidence that QMA(2) is contained in PSPACE, by
showing that this would follow from "strong amplification" of QMA(2)
protocols. Finally, we prove the nonexistence of "perfect
disentanglers" for simulating multiple Merlins with one.
Fri, 02 May 2008 20:53:36 +0300https://eccc.weizmann.ac.il/report/2008/051