  Optimal quantum machines can be implemented by linear projective operations.
In the present work a general qubit symmetrization theory is presented by
investigating the close links to the qubit purification process and to the
programmable teleportation of any generic optimal anti-unitary map. In
addition, the contextual realization of the N ->M cloning map and of the
teleportation of the N->(M-N) universal NOT gate is analyzed by a novel and
very general angular momentum theory. An extended set of experimental
realizations by state symmetrization linear optical procedures is reported.
These include the 1->2 cloning process, the UNOT gate and the quantum
tomographic characterization of the optimal partial transpose map of
polarization encoded qubits.
