Corpus ID: 118309233

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

@article{Kribs2003QuantumCW,
  title={Quantum Channels, Wavelets, Dilations and Representations of \$O\_n\$},
  author={D. Kribs},
  journal={arXiv: Operator Algebras},
  year={2003}
}
  • D. Kribs
  • Published 2003
  • Mathematics, Physics
  • arXiv: Operator Algebras
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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