Approximate Private Quantum Channels
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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  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.
Cite this work
Paul Dickinson (2006). Approximate Private Quantum Channels. UWSpace. http://hdl.handle.net/10012/2944