Quantum channels on duals of von Neumann algebras in the Schr" o dinger picture
math.OA, math.FA, quant-ph
Submitted: 2026-08-15
Updated: 2026-09-21
Comments: 8 pages; section 5 added, minor corrections
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
The gist: 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.
Terminology
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.