# Three-Party Entanglement in Tripartite Teleportation Scheme through Noisy Channels - Quantum Physics

Abstract: We have tried to interpret the physical role of the three-tangle and$\pi$-tangle in the real physical information process. For the modelcalculation we adopt the three-party teleportation scheme through the variousnoisy channels. The three parties consist of sender, accomplice and receiver.It is shown that the $\pi$-tangles for the X- and Z-noisy channels vanish at$\kappa t \to \infty$ limit, where $\kappa t$ is a parameter introduced in themaster equation of Lindblad form. In this limit the receiver-s maximum fidelityreduces to the classical limit 2-3. However, this nice feature is notmaintained at the Y- and isotropy-noise channels. For Y-noise channel the$\pi$-tangle vanishes at $0.61 \leq \kappa t$. At $\kappa t = 0.61$ thereceiver-s maximum fidelity becomes 0.57, which is much less than the classicallimit. Similar phenomenon occurs at the isotropic noise channel. We alsocomputed the three-tangles analytically for the X- and Z-noise channels. Theremarkable fact is that the three-tangle for Z-noise channel is exactly samewith the corresponding $\pi$-tangle. In the X-noise channel the three-tanglevanishes at $0.10 \leq \kappa t$. At $\kappa t = 0.10$ the receiver-s fidelitycan be reduced to the classical limit provided that the accomplice performs themeasurement appropriately. However, the receiver-s maximum fidelity becomes8-9, which is much larger than the classical limit. Since the Y- andisotropy-noise channels are rank-8 mixed states, their three-tangles are notcomputed explicitly. Instead, we have derived their upper bounds with use ofthe analytical three-tangles for other noisy channels. Our analysis stronglysuggests that we need different three-party entanglement measure whose value isbetween three-tangle and $\pi$-tangle.

Author: Eylee Jung, Mi-Ra Hwang, DaeKil Park, Sayatnova Tamaryan

Source: https://arxiv.org/