  Light fields can be amplified by measuring the field amplitude reflected at a
beam splitter of reflectivity R and adding a coherent amplitude proportional to
the measurement result to the transmitted field. By applying the quantum
optical realization of this amplification scheme to single photon inputs, it is
possible to clone the polarization states of photons. We show that optimal
cloning of single photon polarization is possible when the gain factor of the
amplification is equal to the inverse squareroot of 1-R.
