  Correlated photons inspire abundance of metrology-related platforms, which
benefit from quantum (anti-) correlations and outperform their classical-light
counterparts. While such demonstrations mainly focus on entanglement, the role
of photon exchange-phase and degree of distinguishability have not been widely
utilized in quantum-enhanced applications. Using an interferometric setup we
show that even at low degree entanglement, when a two-photon wave-function is
coupled to matter, it is encoded with a reliable "which pathway?" information.
An interferometric exchange-phase-cycling protocol is developed, which enables
phase-sensitive discrimination between microscopic interaction histories
(pathways). We find that quantum-light interferometry facilitates utterly
different set of time-delay variables, which are unbound by uncertainty to the
inverse bandwidth of the wave-packet. We illustrate our findings on an exciton
model-system, and demonstrate how to probe intraband dephasing in time-domain
without temporal resolution at the detection. The exotic scaling of multiphoton
coincidence with respect to the applied intensity is discussed.
