Contrasting GHZ and W-state Entanglement Dynamics due to Correlated Markov Noise

Abstract

The ability to preserve multipartite entanglement in noisy environments is central to advancing quantum information processing. In this work, we develop a semiclassical theoretical model of three entangled qubits exposed to local Markov noise environments with tunable statistical correlations between noise sources. We show that such correlations can significantly influence the dynamics of multipartite entanglement, in some cases slowing its decay and, under ideal conditions, even enabling full preservation. Using tripartite negativity as an entanglement measure, we derive analytical results for the GHZ and W states, demonstrating their contrasting responses to correlated and anticorrelated noise. Our analysis identifies regimes in which multipartite entanglement can be sustained despite environmental interactions, offering new insight into how noise correlations may serve as a resource for protecting quantum coherence in multi-qubit systems.

Figures (10)

• Figure 1: Three uncoupled qubits subject to local classical noise that may be statistically correlated.
• Figure 2: The surface of the cubic volume defined in Equation (8) is shown in blue. The plane $\Gamma_{AB}=\Gamma_{AC}$ is shown in pink. Their intersection, the path 'PQRS', is shown in red.
• Figure 3: Tripartite negativity $\mathcal{N}_{ABC}$ for the GHZ state under dephasing noise, plotted along the path PQRS. The GHZ state resists disentanglement most strongly at point $S(-\tfrac{1}{2},-\tfrac{1}{2},-\tfrac{1}{2})$, where the noise environments are equally anticorrelated.
• Figure 4: Tripartite negativity $\mathcal{N}_{ABC}$ for the W state under dephasing noise, plotted along the path PQRS. W state entanglement is most robust at point $Q(1, 1, 1)$, where all noise environments are maximally correlated.
• Figure 5: Pairwise entanglement dynamics $\mathcal{N}_{A|B}$ and $\mathcal{N}_{A|C}$ (left) and $\mathcal{N}_{B|C}$ (right) for the W state under dephasing noise along correlation path PQRS. (Note that $\mathcal{N}_{A|C}$ = $\mathcal{N}_{B|C}$ due to the choice of $\Gamma_{AB}=\Gamma_{AC}$).