  Convex sets of completely positive maps and positive semidefinite kernels are
considered in the most general context of modules over $C^*$-algebras and a
complete charaterization of their extreme points is obtained. As a byproduct,
we determine extreme quantum instruments, preparations, channels, and extreme
autocorrelation functions. Various applications to quantum information and
measurement theories are given. The structure of quantum instruments is
analyzed thoroughly.
