Characterizing Noise Effects on Multipartite Entanglement via Phase-Space Visualization

This paper investigates the behavior of two fundamental types of multipartite entangled states, namely GHZ(3) and W(3) states under Gaussian-distributed amplitude perturbations and White noise model. The Uhlmann-Jozsa fidelity is taken to be the quantitative measure to show the overall degradation of the quantum states, and is implemented via TQIX : a tool specifically designed for quantum state measurement and related applications. While fidelity analysis captures the progressive decay of quantum states under noise, it offers only limited understanding regarding the state decay and doesn't provide a detailed analysis of how entanglement structures respond to noise models. To reveal the phase-space characteristics and nonclassical signatures of three-qubit entangled states, we employ the spin Wigner function using equal-angle projection. This approach reveals a continuous fading of quantum coherence with increasing noise strength, ultimately providing a clear picture of transition toward classical-like behavior in phase space. This combined qualitative-quantitative framework provides deeper understanding of how different entanglement structures respond to noise, offering practical applications for designing and implementing noise resilient protocols in quantum computing, and quantum information processing.