Optimal quantum cloning on a beam splitter

We demonstrate how a beam splitter in combination with different light sources can be used as an optimal universal 1-->2 quantum cloner and as an optimal universal quantum NOT machine for the polarization qubit of a single photon. For the cloning a source of single photons with maximally mixed polarization is required and for the NOT operation a source of maximally entangled photon pairs. We demonstrate both operations with near optimal fidelity. Our scheme can be generalized in a natural way to clone and NOT the spin state of electrons.