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• W1522529429 abstract "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." @default.
• W1522529429 created "2016-06-24" @default.
• W1522529429 creator A5020769134 @default.
• W1522529429 date "2011-01-01" @default.
• W1522529429 modified "2023-09-23" @default.
• W1522529429 title "Impossibility of Succinct Quantum Proofs for Collision-Freeness." @default.
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