  The Solovay-Kitaev theorem allows us to approximate any single-qubit gate to
arbitrary accuracy with a finite sequence of fundamental operations from a
universal set of gates. Inspired by this decomposition, we present a quantum
channel simulator capable of implementing any completely positive
trace-preserving map. Our realization consists of one ancillary qubit, encoded
in the transverse mode of a laser beam (orbital degree of freedom), one qubit
system, encoded in its polarization (spin), one spin-orbit CNOT gate and four
single-qubit operations performed with prisms and polarization components. Our
results describe the implementation of arbitrary single-qubit channels on the
photon polarization using the transverse mode as the ancillary qubit.
