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Approximate Private Quantum Channels

This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for &epsilon;-randomizing maps, <em>n</em> + 2log(1/&epsilon;) + <em>c</em> bits required to &epsilon;-randomize an arbitrary <em>n</em>-qubit state by improving a scheme of Ambainis and Smith [5] based on small bias spaces [16, 3]. We show by a probabilistic argument that in fact the great majority of random schemes using slightly more than this many bits of key are also &epsilon;-randomizing. We provide the first known nontrivial lower bound for &epsilon;-randomizing maps, and develop several conditions on them which we hope may be useful in proving stronger lower bounds in the future.

Identiferoai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/2944
Date January 2006
CreatorsDickinson, Paul
PublisherUniversity of Waterloo
Source SetsUniversity of Waterloo Electronic Theses Repository
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatapplication/pdf, 367669 bytes, application/pdf
RightsCopyright: 2006, Dickinson, Paul. All rights reserved.

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