Quantum channel locally interacting with environment

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.