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

TL;DR

This paper investigates how the entanglement of specific three-qubit mixed states affects their ability to serve as quantum channels in teleportation, revealing fidelity thresholds below which they become ineffective.

Contribution

It analyzes the entanglement and teleportation fidelity of mixed GHZ and W states, identifying critical fidelity thresholds for their usefulness as quantum channels.

Findings

Entanglement vanishes when fidelity drops below 0.775 for GHZ-based mixtures.

Entanglement vanishes when fidelity drops below 0.833 for W-based mixtures.

Mixed states below these thresholds cannot function as effective quantum teleportation channels.

Abstract

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 $\bar{F}_W \leq 0.833$.