  Qutrits, the triple level quantum systems in various forms, have been
proposed for quantum information processing recently. By the methods presented
in this paper a bi-photonic qutrit, which is encoded with the polarizations of
two photons in the same spatial-temporal mode, can be mapped to a single photon
qutrit in spatial modes. It will make arbitrary unitary operation on such
bi-photonic qutrit possible if we can also realize the inverse map to
polarization space. Among the two schemes proposed in this paper, the one based
only on linear optics realizes an arbitrary U(3) operation with a very small
success probability. However, if added with weak nonlinearity, the success
probability can be greatly improved. These schemes are feasible with the
current experimental technology.
