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IEEE Wireless Communications Letters

A Unified MGF-Based Performance Analysis of Quantum Communications Over Turbulence Channels With Pointing Errors

Yazan H. Al-Badarneh, Osamah S. Badarneh, Mustafa Kamal AlShawaqfeh, Tamer M. Khattab, Mazen O. Hasna

Published Apr 22, 2025• 4 citations
Publisher

Abstract

We investigate the performance of free-space quantum communication systems affected by deterministic losses, atmospheric turbulence, and pointing errors. We first propose a novel and unified MGF-based framework to analyze the performance under optimal quantum hypothesis testing (Helstrom detection). Specifically, we derive an analytical expression for the average error probability and a highly accurate approximate expression for the ergodic capacity, both expressed in terms of the MGF of the equivalent channel transmissivity, which accounts for the combined effects of deterministic losses, atmospheric turbulence, and pointing errors. The derived expressions exhibit excellent concordance with numerical simulations, providing insightful perspectives on the analysis and design of quantum communication systems and can be generally used to evaluate performance under various settings.

DOI
10.1109/lwc.2025.3563192

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We investigate the performance of free-space quantum communication systems affected by deterministic losses, atmospheric turbulence, and pointing errors. We first propose a novel and unified MGF-based framework to analyze the performance under optimal quantum hypothesis testing (Helstrom detection). Specifically, we derive an analytical expression for the average error probability and a highly accurate approximate expression for the ergodic capacity, both expressed in terms of the MGF of the equivalent channel transmissivity, which accounts for the combined effects of deterministic losses, atmospheric turbulence, and pointing errors. The derived expressions exhibit excellent concordance with numerical simulations, providing insightful perspectives on the analysis and design of quantum communication systems and can be generally used to evaluate performance under various settings.
In this letter, we analyze the average probability of error of quantum modulation schemes in weakly turbulent quantum communication channels utilizing coherent states. Atmospheric turbulence-induced fading is a significant challenge that degrades the performance of free-space quantum communication systems. We derive and present closed-form expressions for the average probability of error for various detection methods: classical (shot-noise limited) single-photon detection, coherent detection, and the optimal quantum hypothesis-testing (Helstrom) detection for binary quantum modulation schemes. Our analysis focuses on the transmission of classical data modulated by quantum coherent states over a log-normal turbulent channel. Additionally, we discuss the lower bounds of the average capacities for Helstrom detection, providing comprehensive insights into the achievable information rates in realistic atmospheric conditions. The derived expressions show excellent agreement with numerical Monte Carlo simulations across a broad range of average transmitted photon numbers, offering valuable guidelines for the design and optimization of quantum communication systems.
We develop an exact error probability framework for quantum free space optics (FSO) communication over atmospheric channels with turbulence and pointing errors under a physically admissible bounded transmissivity model. The proposed framework is grounded in the fundamental physical observation that, in a quantum optical channel, the random channel quantity is the transmissivity itself, namely, the fraction of transmitted photons collected at the receiver, and must therefore take values only in the physically admissible interval [0,1]. This constraint is generally violated when classical turbulence models are interpreted directly as transmissivity models in quantum settings. Accordingly, we model the turbulence-induced transmissivity as a Beta distributed random variable over (0,1), which has recently been shown to provide accurate fitting under different turbulence conditions while preserving physical admissibility. We then integrate deterministic atmospheric loss and pointing errors into a unified equivalent transmissivity model and derive exact expressions for its probability density function and moment generating function. Building upon this statistical characterization, we derive novel exact average error probability expressions for binary modulation under both quantum and classical receivers. Finally, we verify the analysis using Monte Carlo simulations, quantify the impact of turbulence and pointing errors, and demonstrate the performance advantage of quantum optimal detection in photon-limited quantum FSO channels.
This paper investigates the performance of coherent-state quantum optical wireless communication systems operating over atmospheric turbulence channels with pointing errors (PEs). The average error probability (AEP) and average achievable rate (AAR) are analyzed for on–off keying (OOK) and binary phase-shift keying (BPSK) signaling under photon-counting (PC), homodyne, and optimal Helstrom detection. The proposed framework jointly incorporates deterministic path loss, atmospheric turbulence, and PEs, and accommodates multiple statistical channel models, including Gamma-Gamma (GG), doubly inverted Gamma-Gamma (IGGG), and Fisher-Snedecor FFF distributions, within a unified analytical formulation. Closed-form expressions for AEP and AAR are derived via direct probability density function (PDF)-based integration of the conditional error probability, along with high-photon-number asymptotic approximations that provide insight into performance scaling behavior. Numerical results validate the analytical expressions and demonstrate the impact of PEs on system performance. The analysis further enables systematic comparison between classical and optimal quantum detection schemes and quantifies the achievable performance gains under different channel conditions. These results provide useful design insights for modulation and receiver selection in turbulent free-space optical (FSO) communication systems.
This paper develops a comprehensive analytical framework for a time-switching decode-and-forward quantum relay-assisted free-space optical communication system. In the proposed architecture, a batteryless relay harvests optical energy during a dedicated fraction of each transmission block and forwards quantum coherent states during the remaining time, enabling self-sustainable quantum relaying. Both hops are subject to Gamma-Gamma distributed atmospheric turbulence and additive Gaussian detection noise, while the relay and destination implement Helstrom-optimal quantum measurements that achieve the minimum symbol detection error. The framework unifies the effects of energy harvesting, turbulence-induced fading, and quantum-limited detection within a single performance model. Closed-form analytical expressions are derived for binary phase-shift keying modulation using the Helstrom bound, enabling tractable evaluation of the end-to-end error probability and the effective rate. The analysis establishes that the effective rate exhibits a strictly unimodal dependence on the harvesting fraction, yielding a unique optimal operating point that maximizes throughput under energy and noise constraints. Numerical results validate the theoretical findings and quantify the impact of turbulence severity, detection noise, and harvesting efficiency, demonstrating substantial performance gains over conventional non-harvesting quantum relays and providing new insights for energy-autonomous quantum optical networks.
This paper develops a comprehensive analytical framework for a time-switching decode-and-forward quantum relay-assisted free-space optical communication system. In the proposed architecture, a batteryless relay harvests optical en ergy during a dedicated fraction of each transmission block and forwards quantum coherent states during the remaining time, enabling self-sustainable quantum relaying. Both hops are subject to Gamma–Gamma distributed atmospheric turbulence and additive Gaussian detection noise, while the relay and destination implement Helstrom-optimal quantum measurements that achieve the minimum symbol detection error. The frame work unifies the effects of energy harvesting, turbulence-induced fading, and quantum-limited detection within a single performance model. Closed-form analytical expressions are derived for binary phase-shift keying modulation using the Helstrom bound, enabling tractable evaluation of the end-to-end error probability and the effective rate. The analysis establishes that the effective rate exhibits a strictly unimodal dependence on the harvesting fraction, yielding a unique optimal operating point that maximizes throughput under energy and noise constraints. Numerical results validate the theoretical findings and quantify the impact of turbulence severity, detection noise, and harvesting efficiency, demonstrating substantial performance gains over conventional non-harvesting quantum relays and providing new insights for energy-autonomous quantum optical networks
This paper presents a comprehensive analysis on capacity of free space optics (FSO) for classical and quantum communications, since FSO is one of enabler technologies for the sixth generation (6G) of telecommunication, of which the understanding on the differences between classical and quantum channel capacity becomes critical to support the future development. The classical channel models, assuming the effects of atmospheric turbulence in the irradiance distribution, is analyzed both computationally and analytically through closed-form expressions. On the other hands, quantum channel models are analyzed by taking into account the probability of errors caused by turbulence. This paper reveals that the turbulence significantly degrades the capacity of the classical channel compared to the quantum channel; however the degrades in quantum channel is less extreme. Remarkably, none of the quantum channel models experience a drastic drop to zero capacity, where 4 out of 6 models are consistently maintaining non-zero capacity performances.