Distances for Operator-valued Information Channels
Operator Algebras
2024-09-26 v1
Abstract
We introduce three metrics on the set of quantum probability measures over a compact Hausdorff space and characterize them in terms of the completely bounded norm of the corresponding unital completely positive maps. We extend the existing topological structures between scalar-valued information channels to operator-valued ones and associate them with topologies on the set of unital completely positive maps between a commutative C*-algebra and the C*-algebra of bounded weakly measurable operator-valued functions over a compact Hausdorff space. Given a measure on the input alphabet space, we introduce the notion of an almost everywhere defined operator-valued information channel and provide a characterization result.
Cite
@article{arxiv.2409.17052,
title = {Distances for Operator-valued Information Channels},
author = {Georgios Baziotis},
journal= {arXiv preprint arXiv:2409.17052},
year = {2024}
}