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.
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.
Quantum information processing leverages the principles of quantum mechanics, utilizing qubits, to improve computational and communicative tasks. In this realm, the quantum channel’s capacity is pivotal in determining the efficiency and accuracy of quantum information handling, with its performance being significantly influenced by channel noise. Our study aims to establish a holistic hybrid quantum noise model to determine the quantum channel capacity. In this paper, we formulated a mathematical expression for this capacity and conducted simulations for both Gaussian and non-Gaussian inputs. A hybrid noise model is constructed by convolution of Poisson-distributed quantum noise with classical additive white Gaussian noise. We characterized the quantum-classical noise and the received signal using Gaussian Mixture Models. The maximum amount of quantum information that can be reliably transmitted over a quantum channel (per use of the channel) is determined by its capacity, and entropy and related quantities like mutual information play a role in calculating this capacity. Our formulation of quantum channel capacity is derived from the mutual information shared between the transmitter and receiver, encompassing the entropies of the signals. The quantum channel presents a higher capacity-to-signal-to-noise ratio for Gaussian inputs than non-Gaussian ones.
Quantum communication systems are essential for secure information transmission, but their performance is significantly impeded by complex hybrid quantum noise (HQN) in Gaussian quantum channels. Accurately modeling this noise is crucial for optimizing channel achievable rates, a problem compounded by the complex nature of hybrid noise, which combines quantum shot noise and classical additive-white-Gaussian noise (AWGN) and is typically represented as an infinite mixture of Gaussian distributions. This work focuses on optimizing the HQN model to improve the achievable rate of Gaussian quantum channels using Machine Learning (ML) optimized clusters. The work specifically leverages Gaussian mixture model (GMM) and the Expectation-Maximization (EM) algorithm to model the complex noise characteristics of quantum channels. The study proposes modeling of hybrid noise as an infinite mixture of Gaussian distributions weighted by Poissonian parameters, with a novel cluster reduction technique that minimizes the number of Gaussian components while maintaining accuracy within acceptable error tolerances. Simulation results demonstrate that the GMM-EM enhanced clustering method significantly improves channel achievable rates in general quantum communication and satellite-based quantum communication systems. The GMMEM method substantially outperforms conventional clustering techniques, including K-means and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithms, in terms of maximizing achievable rates and characterizing noise accuracy. This advancement provides a practical and efficient solution for real-time quantum noise modeling, representing a significant improvement over existing state-of-the-art approaches in quantum communication network optimization
For a continuous-input-continuous-output arbitrarily distributed quantum channel carrying classical information, the channel capacity can be computed in terms of the distribution of the channel envelope, received signal strength over a quantum propagation field and the noise spectral density. If the channel envelope is considered to be unity with unit received signal strength, the factor controlling the capacity is the noise. Quantum channel carrying classical information will suffer from the combination of classical and quantum noise. Assuming additive Gaussian-distributed classical noise and Poisson-distributed quantum noise, we formulate a hybrid noise model by deriving a joint Gaussian- Poisson distribution in this letter. For the transmitted signal, we consider the mean of signal sample space instead of considering a particular distribution and study how the maximum mutual information varies over such mean value. Capacity is estimated by maximizing the mutual information over unity channel envelope.
This research advances the application of QKD in FSO satellite-based quantum communication. It proposes an innovative satellite quantum channel model and derives the secret quantum key distribution rate achievable through this channel. Unlike existing models that approximate the noise in quantum channels as merely Gaussian distributed, this model incorporates a hybrid quantum noise analysis, accounting for both quantum Poissonian noise and classical AWGN. This hybrid approach acknowledges the dual vulnerability of CV Gaussian quantum channels to both quantum and classical noise under collective attack with RR setting, thereby offering a more realistic assessment of the quantum SKR. This work delves into the variation of asymptotic SKR with the SNR and satellite altitudes under various influencing parameters. We identify and analyze critical factors such as reconciliation efficiency, electrical noise, transmission coefficient, detection efficiency, transmission efficiency, excess noise, and the quantum Poissonian noise parameter impacting the SKR. These parameters are pivotal in determining the asymptotic SKR in FSO satellite quantum channels, highlighting the challenges of satellite-based quantum communication. A comparative study has been provided based on the finite-size and asymptotic SKR. It provides a comprehensive framework for understanding and optimizing asymptotic SKR in satellite-based QKD systems, paving the way for more efficient and secure quantum communication networks.
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.
This paper develops a hybrid quantum channel model tailored for finite-regime quantum key distribution (QKD) in free-space satellite quantum communication. The channel model addresses the fading characteristics of satellite-to-ground links while incorporating the dynamics of satellite orbits. By conducting a comprehensive security analysis under finite-size effects and collective attacks, the research bridges the theoretical and practical aspects of satellite-based QKD. Critical parameters, such as reconciliation efficiency, transmission coefficient, detection efficiency, receiver telescope aperture, beam waist, and effective communication time, are systematically investigated to optimize the secret key rate. The study reveals key trade-offs between the influence of satellite altitude on communication windows, noise levels, and synchronization, which significantly impact quantum channel efficiency. The model improves the accuracy of free-space quantum channel evaluations by presenting a hybrid noise framework that combines quantum Poissonian noise with classical additive white Gaussian noise (AWGN). Our numerical results demonstrate the feasibility and robustness of finite-regime QKD for uplink and downlink configurations in various atmospheric conditions, highlighting the superiority of satellite-based quantum communication over conventional networks.