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

Proceedings of the Edinburgh Mathematical Society

David W. Kribs¹ 

关键词: operator;    completely positive map;    quantum channel;    orthogonal wavelet;    isometric dilation;    Cuntz algebra;   

DOI  :  10.1017/S0013091501000980

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We 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

【 授权许可】

Unknown