The Choi-Jamiolkowski isomorphism and covariant quantum channels

Understand

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.