Three-party entanglement in tripartite teleportation scheme through noisy channels

In this paper we have tried to interpret the physical role of the three-tangle and π-tangle in the real physical information process. For the model calculation we adopt the three-party teleportation scheme through the various noisy channels. The three parties consist of sender, accomplice and receiver. It is shown that the π-tangles for the X-and Z-noisy channels vanish at κt → ∞ limit, where κt is a parameter introduced in the master equation of Lindblad form. In this limit the receiver's maximum fidelity reduces to the classical limit 2/3. However, this nice feature is not maintained at the Y-and isotropy-noise channels. For Y-noise channel the π-tangle vanishes at 0.61 ≤ κt. At κt = 0.61 the receiver's maximum fidelity becomes 0.57, which is much less than the classical limit. Similar phenomenon occurs at the isotropic noise channel. We also computed the three-tangles analytically for the X-and Z-noise channels. The remarkable fact is that the three-tangle for Z-noise channel is exactly same with the corresponding π-tangle. In the X-noise channel the three-tangle vanishes at 0.10 ≤ κt. At κt = 0.10 the receiver's fidelity can be reduced to the classical limit provided that the accomplice performs the measurement appropriately. However, the receiver's maximum fidelity becomes 8/9, which is much larger than the classical limit. Since the Y-and isotropy-noise channels are rank-8 mixed states, their three-tangles are not computed explicitly in this paper. Instead, we have derived their upper bounds with use of the analytical three-tangles for other noisy channels. Our analysis strongly suggests that we need different three-party entanglement measure whose value is between three-tangle and π-tangle.