Quantum cloning in spin networks

We introduce an approach to quantum cloning based on spin networks and we demonstrate that phase covariant cloning can be realized using no external control but only with a proper design of the Hamiltonian of the system. In the $1\to 2$ cloning we find that the $XY$ model saturates the value for the fidelity of the optimal cloner and gives values comparable to it in the general $N\to M$ case. We finally discuss the effect of external noise. Our protocol is much more robust to decoherence than a conventional procedure based on quantum gates.