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

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 moment generating function (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.