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

David W. Kribs
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Abstract

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.

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David W. Kribs. 2003-09-23. Quantum Channels, Wavelets, Dilations and Representations of $O_n$. https://arxiv.org/abs/math/0309390

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