  A family of quantum cloning machines is introduced that produce two
approximate copies from a single quantum bit, while the overall input-to-output
operation for each copy is a Pauli channel. A no-cloning inequality is derived,
describing the balance between the quality of the two copies. This also
provides an upper bound on the quantum capacity of the Pauli channel with
probabilities $p_x$, $p_y$ and $p_z$. The capacity is shown to be vanishing if
$(\sqrt{p_x},\sqrt{p_y},\sqrt{p_z})$ lies outside an ellipsoid whose pole
coincides with the depolarizing channel that underlies the universal cloning
machine.
