A Mathematical Framework for a Lunar-to-Mars Quantum Key Distribution Architecture

This paper presents a parameter-strict, validated mathematical framework for a directLunar-to-Mars interplanetary quantum key distribution (QKD) link operating over a deep-spacevacuum baseline with atmospheric termination. By enforcing a 2D polarization-encoded qubit mapping(BB84/BBM92), we map dynamic channel vulnerabilities including astrodynamic scale drift, planetaryatmospheric noise, tracking system vibrations, and atmospheric scattering phase errors. A corecontribution of this work is the integration of a true quantum depolarizing channel model with anAdaptive Temporal Scaling (ATS) framework. This integration establishes realistic operational boundsunder the standard Shor-Preskill security threshold with a realistic error correction efficiency overheadfactor (f = 1.20), accurately predicting link capacity scaling and absolute cryptographic blackoutscaused by Martian dust storm scattering without relying on vulnerable multi-hop relays.