  A linear map $L$ from ${\mathbb C}^{n \times n}$ into ${\mathbb C}^{n \times
n}$ is called a quantum channel if it is completely positive and trace
preserving. The set ${\cal L}_n$ of all such quantum channels is known to be a
compact convex set. While the extreme points of ${\cal L}_n$ can be
characterized, not much is known about the structure of its higher dimensional
faces. Using the so called Choi matrix $Z(L)$ associated with the quantum
channel $L$, we compute the maximum dimension of a proper face of ${\cal L}_n$,
and in addition the possible dimensions of faces generated by $L$ when $rank \
Z(L)=2 $.
