Optimal phase-covariant cloning for qubits and qutrits

We consider cloning transformations of equatorial qubits |ψ_φ〉=1/√2(|0〉+e^iφ|1〉) and qutrits |ψ_φ,θ〉=1/√3(|0〉+e^iφ|1〉+e^iθ|2〉), with the transformation covariant for rotation of the phases φ and θ. The optimal cloning maps are derived without simplifying assumptions from first principles, for any number of input and output qubits, and for a single-input qutrit and any number of output qutrits. We also compare the cloning maps for global and single-particle fidelities, and we show that the two criteria lead to different optimal maps.