The lower bound to the concurrence for four-qubit W state under noisy channels

TL;DR

This paper analytically examines how four-qubit W states lose entanglement under different noisy environments, revealing that some noise types cause sudden decay while others lead to gradual loss, and compares robustness across states.

Contribution

It provides an analytical study of the entanglement dynamics of four-qubit W states under various Pauli noise channels, highlighting differences in robustness and decay patterns.

Findings

Entanglement decays monotonically under Pauli-Z noise.

Entanglement exhibits sudden death under other Pauli noises.

Four-qubit W state is more robust than other states under same-axis Pauli channels.

Abstract

We study the dynamics of four-qubit W state under various noisy environments by solving analytically the master equation in the Lindblad form in which the Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Also, we investigate the dynamics of the entanglement using the lower bound to the concurrence. It is found that while the entanglement decreases monotonically for Pauli-Z noise, it decays suddenly for other three noises. Moreover, by studying the time evolution of entanglement of various maximally entangled four-qubit states, we indicate that the four-qubit W state is more robust under same-axis Pauli channels. Furthermore, three-qubit W state preserves more entanglement with respect to the four-qubit W state, except for the Pauli-Z noise.