Sciweavers

Share
CORR
2011
Springer

Impossibility of Succinct Quantum Proofs for Collision-Freeness

8 years 12 days ago
Impossibility of Succinct Quantum Proofs for Collision-Freeness
We show that any quantum algorithm to decide whether a function f : [n] → [n] is a permutation or far from a permutation must make Ω n1/3 /w queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a permutation. This implies that there exists an oracle A such that SZKA ⊂ QMAA , answering an eight-year-old open question of the author. Indeed, we show that relative to some oracle, SZK is not in the counting class A0PP defined by Vyalyi. The proof is a fairly simple extension of the quantum lower bound for the collision problem.
Scott Aaronson
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Scott Aaronson
Comments (0)
books