  The quantum channel subject to local interaction with two-level environment
is studied. The two-level environment is regarded as a quantum bit (qubit) as
well as a pair of particles owned by Alice and Bob. The amount of entanglement
initially shared by Alice and Bob is distributed among these three qubits due
to the interaction. In this model, we show that the singlet fraction of the
decohered quantum channel is uniquely determined by the distributed
entanglement. When the decohered quantum channel is used under the standard
teleportation scheme, the optimal teleportation fidelity is well understood by
considering the remaining entanglement between environment and transmitted
state.
