Mixed-State Entanglement and Quantum Teleportation through Noisy Channels

TL;DR

This paper analyzes how noisy entangled states affect quantum teleportation, showing that entanglement measures vanish below a fidelity threshold, emphasizing entanglement's role as a physical resource, with insights into higher-qubit states.

Contribution

It provides analytical results linking entanglement measures to teleportation fidelity and explores optimal decompositions for noisy multi-qubit states, including W-states.

Findings

Entanglement measures vanish when average fidelity ≤ 2/3.

Entanglement is essential for successful quantum teleportation.

Optimal decompositions for three-qubit mixed states are discussed.

Abstract

The quantum teleportation with noisy EPR state is discussed. Using an optimal decomposition technique, we compute the concurrence, entanglement of formation and Groverian measure for various noisy EPR resources. It is shown analytically that all entanglement measures reduce to zero when $\bar{F} \leq 2/3$, where $\bar{F}$ is an average fidelity between Alice and Bob. This fact indicates that the entanglement is a genuine physical resource for the teleportation process. This fact gives valuable clues on the optimal decomposition for higher-qubit mixed states. As an example, the optimal decompositions for the three-qubit mixed states are discussed by adopting a teleportation with W-state