Abstract
We consider cloning transformations of d-dimensional states of the form e^{iϕ_0}|0> + e^{iϕ_1}|1> +...+ e^{iϕ_{d-1}}|d-1> that are covariant with respect to rotations of the phases ϕ_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.
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