  Let L(m,n) denote the convex set of completely positive trace preserving
operators from C^{m x m} to C^{n x n}$, i.e quantum channels. We give a
necessary condition for L in L(m,n) to be an extreme point. We show that
generically, this condition is also sufficient. We characterize completely the
extreme points of L_(2,2) and L(3,2), i.e. quantum channels from qubits to
qubits and from qutrits to qubits.
