  We consider cloning transformations of d-dimensional states of the form
e^{i\phi_0}|0> + e^{i\phi_1}|1> +...+ e^{i\phi_{d-1}}|d-1> that are covariant
with respect to rotations of the phases \phi_i's. The optimal cloning maps are
easily obtained using a well-defined general characterization of
state-dependent 1 -> 2 cloning transformations in arbitrary dimensions. Our
results apply to symmetric as well as asymmetric cloners, so that the balance
between the fidelity of the two clones can be analyzed.
