Doppler effect on dual-downlink time-bin quantum key distribution and a proposed ephemeris-assisted witness-field correction

Time-bin entanglement is promising for satellite Quantum Key Distribution (QKD) due to its compatibility with telecom fiber networks, but its phase-sensitive measurements are vulnerable to Doppler effects induced by satellite motion. We present a spectral-temporal framework for time-bin-entangled photon pairs generated onboard a satellite via Spontaneous Parametric Down-Conversion (SPDC) and distributed to two Optical Ground Stations (OGSs) over independent downlinks with distinct Doppler shifts. Each OGS is equipped with an Unbalanced Mach-Zehnder Interferometer (UMZI) used to perform Bennett-Brassard-Mermin 1992 (BBM92) entangled-photon QKD. In a simulated Low Earth Orbit (LEO) pass with matched 400 ps analyzer delays, the received time-bin separation changes by at most 8.8 fs per link, while the combined carrier phase shifts by about 38 rad, which primarily degrades phase-basis correlations. After zero-Doppler calibration, this phase separates into independent signal- and idler-link contributions, allowing each station to correct its link Doppler phase shift locally, without real-time phase exchange between the stations. We propose an ephemeris-assisted feed-forward architecture, in which an auxiliary interferometer analyzes a co-propagating classical witness field to reconstruct the local Doppler-induced phase, which a phase modulator then compensates on the quantum channel. In a noise-free model, a 1 Hz sample-and-hold correction rate keeps the phase-basis Quantum Bit Error Rate (QBER) below 2% and retains 93% of the ideal asymptotic key yield. After 18 accumulated passes, the corrected finite secret key reaches 95% of its ideal length, whereas relabeling the parity from the ephemeris without optical correction reaches only about 8%.