Hybrid Quantum Noise Model for Gaussian Quantum Channels: Development, Optimization, and Applications

Abstract

Quantum Gaussian channels are fundamental to the secure and efficient transmission of quantum information; however, quantum noise significantly impacts their performance in computing, cryptography, and communication. This research develops, optimizes, and validates a hybrid quantum noise model (HQNM) to enhance the understanding of quantum Gaussian channels. The study is structured into three parts: (I) Model Development and Analysis, where a hybrid quantum noise model combining Poissonian noise and classical additive white Gaussian noise (AWGN) is introduced. Closed-form capacity expressions are derived, confirming that Gaussian inputs achieve the highest data rates across different signal-to-noise ratios (SNR). The hybrid noise is modeled as a finite Gaussian mixture with Poisson-distributed weights, providing deeper insights into noise structure and optimization. Graphical representations enhance visualization, showing correlations between quantum Poissonian noise and classical AWGN. Additionally, entropy-based analysis refines the estimation of quantum channel capacity, offering more profound insights into entropy-driven noise effects. (II) Optimization and Validation incorporate machine learning (ML) techniques to improve quantum noise modeling. Hybrid noise is reformulated as a Gaussian mixture model (GMM), with the Expectation-Maximization (EM) algorithm dynamically updating channel parameters for optimal noise clustering. ML-based refinements significantly enhance capacity estimation and noise compensation, thereby improving signal accuracy across a range of SNR levels. (III) Applications in quantum key distribution (QKD) extend the HQN framework to satellite-based QKD, integrating quantum Poissonian noise and AWGN into a free-space quantum channel model. The study evaluates SKR performance under different reconciliation efficiencies, SNRs, and satellite altitudes, introducing a finite-regime QKD analysis. The findings establish a foundational framework for optimizing quantum communication, bridging the gap between theoretical noise models and real-world satellite quantum networks.