Optimal nonuniversally covariant cloning

We consider nonuniversal cloning maps, namely, cloning transformations that are covariant under a proper subgroup G of the universal unitary group $U\left(d\right),$ where d is the dimension of the Hilbert space $\mathcal{H}$ of the system to be cloned. We give a general method for optimizing cloning for any cost function. Examples of applications are given for phase-covariant cloning (cloning of equatorial qubits and qutrits) and for the Weyl-Heisenberg group (cloning of “continuous variables”).