Topology-assisted balanced two-parameter metrology with four-photon boundary correlations

Post-selected four-photon boundary correlations in a quadratic Su-Schrieffer-Heeger waveguide array are studied as a resource for topology-assisted two-parameter quantum metrology. Two pumped channels generate two nondegenerate spontaneous parametric down-conversion biphoton pairs whose indistinguishable four-photon amplitudes interfere to form a post-selected cluster-like path-encoded boundary probe. Separable, pair-product, and full four-photon probes are compared to separate single-particle boundary localization, pair-product boundary correlations, and genuine four-photon exchange interference, showing that the high-sensitivity window is mainly established by topology-supported pair correlations and further enhanced by exchange coherence. At a representative operating point, the optimized sensitivity increases with exchange coherence and remains operational under moderate onsite disorder. These results identify topological four-photon boundary correlations as a compact and robust platform for balanced two-parameter quantum metrology.