A Theoretical Framework for an Earth-to-Moon Quantum Uplink Architecture

This paper presents a parameter-strict mathematical framework for a directEarth-to-Moon quantum communication uplink. Rather than relying on empiricalefficiency constants, we simulate geometric loss via fundamental wave optics andspatial diffraction bounds using a 5 GHz weak coherent pulse laser source. Weincorporate a physically rigorous Core-Halo wavefront power distribution modelcombined with a ground Adaptive Optics (AO) system operating at 1550 nm (TelecomC-band) to overcome boundary-layer atmospheric turbulence at a high-elevationterminal in Hanle, Ladakh. Anisoplanatic effects induced by a 3.5 µrad point-aheadangle are factored in, yielding a realistic post-correction Strehl ratio of S = 0.86.Incorporating a high-efficiency Superconducting Nanowire Single-Photon Detector(SNSPD) layout combined with a 200 ps temporal gating window and narrowbandspectral filters on the lunar receiver, we evaluate system survival under stochasticlog-normal atmospheric fading using the Decoy-State GLLP asymptotic bound. Thearchitecture explicitly accounts for high-frequency micro-vibrations from aspace-qualified lunar micro-cryocooler by using an isolated optical bench, andmitigates high-altitude wind shear via a 5 kHz fast-loop AO layout. Our Monte Carlosimulations demonstrate that a mean of 402.64 photons/sec are successfullyregistered by a 0.5-meter lunar telescope, generating a resilient, physically verifiablesecure key transmission rate of 84.31 bits/sec under a realistic 2.8439% mean QBERthreshold.