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

This paper introduces a statistical framework for analyzing quantum noise in amplitude-encoded images through perturbation-level statistical modeling. Amplitude-encoded image states are subjected to amplitude damping, phase damping, and depolarizing noise at multiple noise levels, and the resulting perturbations are modeled using a bounded-domain one-parameter Ola distribution. The model parameter is estimated by maximum likelihood and used as a scalar indicator of perturbation concentration, while goodness-of-fit is evaluated using the Kullback?Leibler divergence, the mean absolute error, and a likelihood-based criterion. Results across multiple images and noise levels show that the fitted model provides a simple and interpretable statistical description of perturbation behavior, reveals clear channel-dependent differences in perturbation concentration and spread, and remains competitive relative to alternative one-parameter bounded distributions. These findings suggest that perturbation-domain statistical modeling offers a practical and promising approach for analyzing quantum noise in amplitude-encoded image representations.