Multi-Parameter Error Mitigation in Parametric Down-Conversion via SU(1, 1) Composite Segmentation

Here, we analyze error mitigation in spontaneous parametric down-conversion using composite segmentation governed by SU(1, 1) spatial dynamics. We show that odd spatial Fourier harmonics preserve error-cancellation flatness with pair-generation rates scaling asymptotically as $m^{-2}$, while a coordinate-dilation symmetry provides a design prescription for translating configurations across distinct operating wavelengths (405, 532, and 775 nm).

Furthermore, an open-loop thermo-optic bias counteracts off-axis angular drift to broaden the 90%-efficiency angular acceptance half-width by 3.46x, and up to two missing poling domains are tolerated with no numerically resolved loss in relative conversion efficiency. Across a 5$^\circ$C thermal window, the generated pairs sustain a relative conversion efficiency of $η\ge 0.954$ with the modeled phase-coherence metric remaining above 0.95, providing a structurally robust approach for entangled photon generation without requiring continuous closed-loop feedback stabilization.