  A generalization of the Choi-Jamiolkowski isomorphism for completely positive
maps between operator algebras is introduced. Particular emphasis is placed on
the case of normal unital completely positive maps defined between von Neumann
algebras. This generalization is applied especially to the study of maps which
are covariant under actions of a symmetry group. We highlight with the example
of, e.g., phase-shift-covariant quantum channels the ease of this method in
particular in the case of a compact symmetry group. We also discuss the case of
channels which are covariant under actions of the Euclidean group of rigid
motions in 3 dimensions.
