  The cloning of continuous quantum variables is analyzed based on the concept
of Gaussian cloning machines, i.e., transformations that yield copies that are
Gaussian mixtures centered on the state to be copied. The optimality of
Gaussian cloning machines that transform N identical input states into M output
states is investigated, and bounds on the fidelity of the process are derived
via a connection with quantum estimation theory. In particular, the optimal
N-to-M cloning fidelity for coherent states is found to be equal to
MN/(MN+M-N).
