QUANTUM CHANNELS, WAVELETS, DILATIONS AND REPRESENTATIONS OF $\mathcal{O}_{n}$
2003 ◽
Vol 46
(2)
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pp. 421-433
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Keyword(s):
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
1979 ◽
Vol 86
(1)
◽
pp. 41-55
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2005 ◽
Vol 02
(03)
◽
pp. 251-258
2016 ◽
Vol 3
(4)
◽
pp. 400-410
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