Entanglement dynamics of three-qubit states in noisy channels

TL;DR

This paper investigates how three-qubit entangled states, specifically GHZ and W states, degrade under different noisy channels, revealing that W states are more robust in some channels while GHZ states are more resistant in others.

Contribution

It provides a comparative analysis of entanglement decay of GHZ and W states in various Pauli and depolarizing channels using a lower bound for three-qubit concurrence.

Findings

W state retains more entanglement in σ_z channel

GHZ state is more resistant in σ_x, σ_y, and depolarizing channels

Lower bound approximation's accuracy depends on density matrix rank

Abstract

We study entanglement dynamics of the three-qubit system which is initially prepared in pure Greenberger-Horne- Zeilinger (GHZ) or W state and transmitted through one of the Pauli channels $\sigma_z, \, \sigma_x, \, \sigma_y$ or the depolarizing channel. With the help of the lower bound for three-qubit concurrence we show that the W state preserves more entanglement than the GHZ state in transmission through the Pauli channel $\sigma_z$. For the Pauli channels $\sigma_x, \, \sigma_y$ and the depolarizing channel, however, the entanglement of the GHZ state is more resistant against decoherence than the W-type entanglement. We also briefly discuss how the accuracy of the lower bound approximation depends on the rank of the density matrix under consideration.