Optimal nonuniversally covariant cloning
Giacomo Mauro D’Ariano, Paoloplacido Lo Presti · Physical Review A · 2001
We consider nonuniversal cloning maps, namely, cloning transformations that are covariant under a proper subgroup G of the universal unitary group $U(d),$ 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'').