Noisy teleportation of qubit states via the Greenberger－Horne－Zeilinger state or the W state

The effects of distributing entanglement through the amplitude damping channel or the phase damping channel on the teleportation of a single-qubit state via the Greenberger--Horne--Zeilinger state and the W state are discussed. It is found that the average fidelity of teleportation depends on the type and rate of the damping in the channel. For the one-qubit affected case, the Greenberger--Horne--Zeilinger state is as robust as the W state, i.e., the same quantum information is preserved through teleportation. For the two-qubit affected case, the W state is more robust when the entanglement is distributed via the amplitude damping channel; if the entanglement is distributed via the phase damping channel, the W state is more robust when the noisy parameter is small while the Greenberger--Horne--Zeilinger state becomes more robust when it is large. For the three-qubit affected case, the Greenberger--Horne--Zeilinger state is more robust than the W state.