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PreprintCC BY-NC-SA 4.0arXiv

Quantum channels on duals of von Neumann algebras in the Schrödinger picture

  • Sviatoslav V. Dzhenzher
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Abstract

The theory of quantum channels is traditionally studied either on finite-dimensional state spaces or within the Heisenberg picture as completely positive maps on C^*-algebras. In this paper, we consider quantum channels as completely positive maps on the duals of general von Neumann algebras in the Schrodinger picture. We investigate the construction of such channels through Pettis integrals using representations of topological groups.

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Cite

BibTeXRIS
BibTeX
@misc{dzhenzher2026quantum,
  title = {{Quantum channels on duals of von Neumann algebras in the Schrödinger picture}},
  author = {Sviatoslav V. Dzhenzher},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.15116},
  eprint = {2608.15116},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.15116},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Quantum channels on duals of von Neumann algebras in the Schrödinger picture
AU  - Sviatoslav V. Dzhenzher
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2608.15116
UR  - https://arxiv.org/abs/2608.15116
AB  - The theory of quantum channels is traditionally studied either on finite-dimensional state spaces or within the Heisenberg picture as completely positive maps on C^*-algebras. In this paper, we consider quantum channels as completely positive maps on the duals of general von Neumann algebras in the Schrodinger picture. We investigate the construction of such channels through Pettis integrals using representations of topological groups.
ER  -