Uselessness for an Oracle Model with Internal Randomness
Name
Harrow_Uselessness for.pdf
Size
389.02 KB
Format
Adobe PDF
Checksum (MD5)
aff53be765465bcdc0a03d29d65d03b7
Author(s)
Harrow, Aram W.
Rosenbaum, David J.
Date Issued
May 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://dl.acm.org/citation.cfm?id=2638687
