  Measurements on quantum channels are described by so-called process operator
valued measures, or process POVMs. We study implementing schemes of extremal
process POVMs. As it turns out, the corresponding measurement must satisfy
certain extremality property, which is stronger that the usual extremality
given by the convex structure. This property motivates the introduction and
investigation of the A-convex structure of POVMs, which generalizes both the
usual convex and C*-convex structure. We show that extremal points and faces of
the set of process POVMs are closely related to A-extremal points and A-faces
of POVMs, for a certain subalgebra A. We give a characterization of A-extremal
and A-pure POVMs in the Appendix.
