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The Geometry of Single-Qubit Maps

D. K. L. Oi
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Abstract

The physically allowed quantum evolutions on a single qubit can be described in terms of their geometry. From a simple parameterisation of unital single-qubit channels, the canonical form of all such channels can be given. The related geometry can be used to understand how to approximate positive maps by completely-positive maps, such as in the case of optimal eavesdropping strategies. These quantum channels can be generated by the appropriate network or through dynamical means. The Strømer-Woronowisc result can also be understood in terms of this geometry.

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D. K. L. Oi. 2001-06-06. The Geometry of Single-Qubit Maps. https://arxiv.org/abs/quant-ph/0106035

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