Pure Completely Positive Maps As A Dual Object Of $c^{*}$ -Algebras

David Evans, J. T. Lewis

Bart Demoen, Paul Vanheuverzwijn, André F. Verbeure

Kalyanapuram Rangachari Parthasarathy

Uffe Haagerup, Magdalena Musat

Yuichiro Kitajima

Sviatoslav V. Dzhenzher

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.