Probabilities of multiple quantum teleportation

Using quantum teleportation a quantum state can be teleported with a certain probability. Here the probabilities for multiple teleportation are derived, i.e. for the case that a teleported quantum state is teleported again or even more than two times, for the two-dimensional case, e.g., for the two orthogonal directions of the polarization of photons. It is shown that the probability for an exact teleportation, except for an irrelevant phase factor, is 25%, i.e., surprisingly, this result holds for the case of a single teleportation as well as for an arbitrary number of a sequence of teleportations. In the remaining 75% of the cases, unitary transformations occur, which are equivalent to those occurring for a single teleportation except for an irrelevant phase factor.