  Teleportation for pure states, mixed states with standard and optimal
protocols are introduced and investigated systematically. An explicit equation
governing the teleportation of finite dimensional quantum pure states by a
generally given non-local entangled state is presented. For the teleportation
of a mixed state with an arbitrary mixed state resource, an explicit expression
is obtained for the quantum channel associated with the standard teleportation
protocol. The corresponding transmission fidelity is calculated. It is shown
that the standard teleportation protocol is not optimal. The optimal quantum
teleportation is further studied, its fidelity is given and shown to be related
to the fully entangled fraction of the quantum resource, rather than the single
fraction as in the standard teleportation protocol.
