Quantum Channels, Wavelets, Dilations and Representations of $O_n$

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We show that the representations of the Cuntz C$^\ast$-algebras $O_n$ which arise in wavelet analysis and dilation theory can be classified through a simple analysis of completely positive maps on finite-dimensional space. Based on this analysis, an application in quantum information theory is obtained; namely, a structure theorem for the fixed point set of a unital quantum channel. We also include some open problems motivated by this work.
15 pages, preprint version

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Operator Algebras, Quantum Physics, 46L45, 47A20, 46L60, 42C40, 81P15

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http://salesiana.dossiersoluciones.com/handle/123456789/68655

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0309390
 http://arxiv.org/abs/math/0309390
 Proc. Edinburgh Math. Soc. 46 (2003), 421-433

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arXiv