Optimal quantum cloning via spin networks

In this paper we demonstrate that optimal 1→M phase-covariant cloning quantum cloning is available via free dynamical evolution of spin networks. By properly designing the network and the couplings between spins, we show that optimal 1→M phase-covariant cloning can be achieved if the initial state is prepared as a specific symmetric state. Especially, when M is an odd number, the optimal phase-covariant cloning can be achieved without ancillas. Moreover, we demonstrate that the same framework is capable for optimal 1→2 universal cloning