Role of Three-Qubit Mixed-States Entanglement in Teleportation Scheme

The bipartite quantum teleportation with a three-qubit mixture of GHZ and W states as a quantum channel is discussed. When the quantum channel is a mixed state consisting of the GHZ state plus small perturbed W state, the entanglement of the channel becomes zero when the average fidelity $\bar{F}_{GHZ}$ is less than 0.775. This means that the mixed state cannot play an any role as a quantum channel at $\bar{F}_{GHZ} \leq 0.775$. For the case of the mixed state consisting of the W state plus small perturbed GHZ state it turn out that this mixed state cannot play a role as a quantum channel at $\bar{F}_W \leq 0.833$.