QUANTUM CHANNELS, WAVELETS, DILATIONS AND REPRESENTATIONS OF $\mathcal{O}_{n}$

Author:

Kribs David W.

Abstract

AbstractWe show that the representations of the Cuntz $C^*$-algebras $\mathcal{O}_n$ 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, we find an application in quantum information theory; namely, a structure theorem for the fixed-point set of a unital quantum channel. We also include some open problems motivated by this work.AMS 2000 Mathematics subject classification: Primary 46L45; 47A20; 46L60; 42C40; 81P15

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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