Distances for Operator-valued Information Channels
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909325938655232 |
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| author | Baziotis, Georgios |
| author_facet | Baziotis, Georgios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17052 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distances for Operator-valued Information Channels Baziotis, Georgios Operator Algebras 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. |
| title | Distances for Operator-valued Information Channels |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2409.17052 |