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

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

2003-09-23

arxiv.org/abs/math/0309390v1

Proc. Edinburgh Math. Soc. 46 (2003), 421-433

Mathematics

Operator Algebras

15 pages, preprint version

Scientific paper

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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