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Uselessness for an Oracle Model with Internal Randomness

Author(s)
Harrow, Aram W.; Rosenbaum, David J.
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Abstract
We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can be solved by a quantum algorithm using a single query; we show that such infinity-vs-one separations between classical and quantum query complexities can be constructed from much weaker separations. We also give conditions to determine when oracle problems--either in the standard model, or in any of the generalizations we consider--cannot be solved with success probability better than random guessing would achieve. In the oracle model with internal randomness where the goal is to gain any nonzero advantage over guessing, we prove (roughly speaking) that k quantum queries are equivalent in power to 2k classical queries, thus extending results of Meyer and Pommersheim.
Date issued
2014-05
URI
http://hdl.handle.net/1721.1/88450
Department
Massachusetts Institute of Technology. Department of Physics
Journal
Quantum Information & Computation
Publisher
Rinton Press
Citation
Aram W. Harrow and David J. Rosenbaum. 2014. Uselessness for an oracle model with internal randomness. Quantum Info. Comput. 14, 7&8 (May 2014), 608-624.
Version: Author's final manuscript
ISSN
1533-7146

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