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| Title: | Approximate Private Quantum Channels |
| Authors: | Dickinson, Paul |
| Keywords: | Mathematics
quantum
approximate
randomization
cryptography
small bias
epsilon-randomize
independent space |
| Approved Date: | 2006 |
| Date Submitted: | 2006 |
| 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, n + 2log(1/ε) + c bits required to ε-randomize an arbitrary n-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. |
| Department: | Combinatorics and Optimization |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/2944 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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