  Optimal quantum cloning is the process of making one or more copies of an
arbitrary unknown input quantum state with the highest possible fidelity. All
reported demonstrations of quantum cloning have so far been limited to copying
two-dimensional quantum states, or qubits. We report the experimental
realization of the optimal quantum cloning of four-dimensional quantum states,
or ququarts, encoded in the polarization and orbital angular momentum degrees
of freedom of photons. Our procedure, based on the symmetrization method, is
also shown to be generally applicable to quantum states of arbitrarily high
dimension -- or qudits -- and to be scalable to an arbitrary number of copies,
in all cases remaining optimal. Furthermore, we report the bosonic coalescence
of two single-particle entangled states.
