Comparative Analysis of Differential and Collision Entropy for Finite-Regime QKD in Hybrid Quantum Noisy Channels

In this work, a comparative study between three fundamental entropic measures, differential entropy, quantum Renyi entropy, and quantum collision entropy for a hybrid quantum channel (HQC) was investigated, where hybrid quantum noise (HQN) is characterized by both discrete and continuous variables (CV) noise components. Using a Gaussian mixture model (GMM) to statistically model the HQN, we construct as well as visualize the corresponding pointwise entropic functions in a given 3D probabilistic landscape. When integrated over the relevant state space, these entropic surfaces yield values of the respective global entropy. Through analytical and numerical evaluation, it is demonstrated that the differential entropy approaches the quantum collision entropy under certain mixing conditions, which aligns with the Renyi entropy for order $α= 2$. Within the HQC framework, the results establish a theoretical and computational equivalence between these measures. This provides a unified perspective on quantifying uncertainty in hybrid quantum communication systems. Extending the analysis to the operational domain of finite key QKD, we demonstrated that the same $10\%$ approximation threshold corresponds to an order-of-magnitude change in Eves success probability and a measurable reduction in the secure key rate.

On the Achievable Rate of Satellite Quantum Communication Channel using Deep Autoencoder Gaussian Mixture Model

We present a comparative study of the Gaussian mixture model (GMM) and the Deep Autoencoder Gaussian Mixture Model (DAGMM) for estimating satellite quantum channel capacity, considering hybrid quantum noise (HQN) and transmission constraints. While GMM is simple and interpretable, DAGMM better captures non-linear variations and noise distributions. Simulations show that DAGMM provides tighter capacity bounds and improved clustering. This introduces the Deep Cluster Gaussian Mixture Model (DCGMM) for high-dimensional quantum data analysis in quantum satellite communication.

A Hybrid Noise Approach to Modelling of Free-Space Satellite Quantum Communication Channel for Continuous-Variable QKD

This paper significantly advances the application of Quantum Key Distribution (QKD) in Free- Space Optics (FSO) satellite-based quantum communication. We propose an innovative satellite quantum channel model and derive the secret quantum key distribution rate achievable through this channel. Unlike existing models that approximate the noise in quantum channels as merely Gaussian distributed, our model incorporates a hybrid noise analysis, accounting for both quantum Poissonian noise and classical Additive-White-Gaussian Noise (AWGN). This hybrid approach acknowledges the dual vulnerability of continuous variables (CV) Gaussian quantum channels to both quantum and classical noise, thereby offering a more realistic assessment of the quantum Secret Key Rate (SKR). This paper delves into the variation of SKR with the Signal-to-Noise Ratio (SNR) under various influencing parameters. We identify and analyze critical factors such as reconciliation efficiency, transmission coefficient, transmission efficiency, the quantum Poissonian noise parameter, and the satellite altitude. These parameters are pivotal in determining the SKR in FSO satellite quantum channels, highlighting the challenges of satellitebased quantum communication. Our work provides a comprehensive framework for understanding and optimizing SKR in satellite-based QKD systems, paving the way for more efficient and secure quantum communication networks.

Hybrid Quantum Noise Approximation and Pattern Analysis on Parameterized Component Distributions

Noise is a vital factor in determining the accuracy of processing the information of the quantum channel. One must consider classical noise effects associated with quantum noise sources for more realistic modelling of quantum channels. A hybrid quantum noise model incorporating both quantum Poisson noise and classical additive white Gaussian noise (AWGN) can be interpreted as an infinite mixture of Gaussians with weightage from the Poisson distribution. The entropy measure of this function is difficult to calculate. This research developed how the infinite mixture can be well approximated by a finite mixture distribution depending on the Poisson parametric setting compared to the number of mixture components. The mathematical analysis of the characterization of hybrid quantum noise has been demonstrated based on Gaussian and Poisson parametric analysis. This helps in the pattern analysis of the parametric values of the component distribution, and it also helps in the calculation of hybrid noise entropy to understand hybrid quantum noise better.

A Machine Learning Approach for Optimizing Hybrid Quantum Noise Clusters for Gaussian Quantum Channel Capacity

This work contributes to the advancement of quantum communication by visualizing hybrid quantum noise in higher dimensions and optimizing the capacity of the quantum channel by using machine learning (ML). Employing the expectation maximization (EM) algorithm, the quantum channel parameters are iteratively adjusted to estimate the channel capacity, facilitating the categorization of quantum noise data in higher dimensions into a finite number of clusters. In contrast to previous investigations that represented the model in lower dimensions, our work describes the quantum noise as a Gaussian Mixture Model (GMM) with mixing weights derived from a Poisson distribution. The objective was to model the quantum noise using a finite mixture of Gaussian components while preserving the mixing coefficients from the Poisson distribution. Approximating the infinite Gaussian mixture with a finite number of components makes it feasible to visualize clusters of quantum noise data without modifying the original probability density function. By implementing the EM algorithm, the research fine-tuned the channel parameters, identified optimal clusters, improved channel capacity estimation, and offered insights into the characteristics of quantum noise within an ML framework.