A One-Parameter Statistical Model for Quantum Noise-Induced Perturbations in Amplitude-Encoded Images

This paper presents a statistical framework for characterizing quantum noise effects in amplitude-encoded images through the analysis of noise-induced amplitude perturbations. Classical grayscale images are encoded as normalized quantum amplitude vectors and subjected to stochastic amplitude damping, phase damping, and depolarizing channels. The resulting perturbations are quantified and modeled using a bounded-domain distribution obtained via a nonlinear transformation of the Ola distribution. A single shape parameter is estimated via maximum-likelihood methods, providing a compact descriptor of perturbation concentration across images, noise channels, and noise levels. Experimental results reveal a consistent decreasing relationship between the estimated parameter and noise level, along with clear channel-dependent statistical signatures. Phase damping, despite producing negligible visual changes in reconstructed images, yields measurable perturbations that are accurately captured by the proposed model. Goodness-of-fit analysis based on Kullback–Leibler divergence, mean absolute error, and likelihood-based criteria demonstrates stable model performance across noise regimes, supported by bootstrap uncertainty analysis. The proposed approach provides a unified and statistically robust representation of quantum noise-induced perturbations in amplitude-encoded images, enabling systematic comparison of noise effects beyond visual inspection. This characterization supports noise-aware quantum image processing by offering a compact, channel-dependent statistical description that can inform algorithm design and evaluation under realistic noise conditions.