Quantum Channels, Wavelets, Dilations and Representations of OnO_n

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.Comment: 15 pages, preprint versio

A quantum computing primer for operator theorists

This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum channels, or equivalently, completely positive trace preserving maps. The main theorems for quantum error detection and correction are presented and we conclude with a description of a particular passive method of quantum error correction.Comment: 24 pages, to appear in Lin. Alg. App