dc.contributor.author | Dickinson, Paul | en |
dc.date.accessioned | 2007-05-08 14:01:52 (GMT) | |
dc.date.available | 2007-05-08 14:01:52 (GMT) | |
dc.date.issued | 2006 | en |
dc.date.submitted | 2006 | en |
dc.identifier.uri | http://hdl.handle.net/10012/2944 | |
dc.description.abstract | This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for ε-randomizing maps, <em>n</em> + 2log(1/ε) + <em>c</em> bits required to ε-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 ε-randomizing. We provide the first known nontrivial lower bound for ε-randomizing maps, and develop several conditions on them which we hope may be useful in proving stronger lower bounds in the future. | en |
dc.format | application/pdf | en |
dc.format.extent | 367669 bytes | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.rights | Copyright: 2006,
Dickinson, Paul. All rights reserved. | en |
dc.subject | Mathematics | en |
dc.subject | quantum | en |
dc.subject | approximate | en |
dc.subject | randomization | en |
dc.subject | cryptography | en |
dc.subject | small bias | en |
dc.subject | epsilon-randomize | en |
dc.subject | independent space | en |
dc.title | Approximate Private Quantum Channels | en |
dc.type | Master Thesis | en |
dc.pending | false | en |
uws-etd.degree.department | Combinatorics and Optimization | en |
uws-etd.degree | Master of Mathematics | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |