  Seeking flexible methods to control quantum teleportation in open systems is
an important task of quantum communication. In this paper, we study how the
super-Ohmic, Ohmic and sub-Ohmic reservoirs affect teleportation of a general
one-qubit state. The results revealed that the structures of the reservoirs
play a decisive role on quality of teleportation. Particularly, the fidelity of
teleportation may be improved by the strong backaction of the non-Markovian
memory effects of the reservoir. The physical mechanism responsible for this
improvement are determined.
