Cloning of spin-coherent states

We consider optimal cloning of the spin coherent states in Hilbert spaces of different dimensionality d. We give explicit form of optimal cloning transformation for spin coherent states in the three-dimensional space, analytical results for the fidelity of the optimal cloning in $d=3$ and $d=4$ as well as numerical results for higher dimensions. In the low-dimensional case we construct the corresponding completely positive maps and exhibit their structure with the help of Jamio{}kowski isomorphism. This allows us to formulate some conjectures about the form of optimal coherent cloning completely positive maps in arbitrary dimension.