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Singularising quantum channels preserving kappa-additivity
Abstract
We construct quantum channels by averaging unitary shift conjugations with respect to κ-additive probability measures on measurable abelian groups. The channels act on the duals of operator algebras generated by shifts and bounded measurable multiplication operators. They preserve κ-additivity of quantum states and admit a weak-* integral representation on this class. If the averaging measure vanishes on singletons, every output state is singular. In the appendix, we also establish the corresponding Fubini's theorem for κ-additive measures.
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BibTeX
@misc{dzhenzher2026singularising,
title = {{Singularising quantum channels preserving kappa-additivity}},
author = {Sviatoslav V. Dzhenzher},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.12537},
eprint = {2611.12537},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.12537},
}
RIS
TY - UNPB
TI - Singularising quantum channels preserving kappa-additivity
AU - Sviatoslav V. Dzhenzher
PY - 2026
DA - 2026/11/09
PB - arXiv
DO - 10.48550/arxiv.2611.12537
UR - https://arxiv.org/abs/2611.12537
AB - We construct quantum channels by averaging unitary shift conjugations with respect to κ-additive probability measures on measurable abelian groups. The channels act on the duals of operator algebras generated by shifts and bounded measurable multiplication operators. They preserve κ-additivity of quantum states and admit a weak-* integral representation on this class. If the averaging measure vanishes on singletons, every output state is singular. In the appendix, we also establish the corresponding Fubini's theorem for κ-additive measures.
ER -