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Correlated photons inspire abundance of metrology-related platforms, whichbenefit from quantum (anti-) correlations and outperform their classical-lightcounterparts. While such demonstrations mainly focus on entanglement, the roleof photon exchange-phase and degree of distinguishability have not been widelyutilized in quantum-enhanced applications. Using an interferometric setup weshow that even at low degree entanglement, when a two-photon wave-function iscoupled to matter, it is encoded with a reliable "which pathway?" information.An interferometric exchange-phase-cycling protocol is developed, which enablesphase-sensitive discrimination between microscopic interaction histories(pathways). We find that quantum-light interferometry facilitates utterlydifferent set of time-delay variables, which are unbound by uncertainty to theinverse bandwidth of the wave-packet. We illustrate our findings on an excitonmodel-system, and demonstrate how to probe intraband dephasing in time-domainwithout temporal resolution at the detection. The exotic scaling of multiphotoncoincidence with respect to the applied intensity is discussed.

Distinguishability and "which pathway" information in multidimensional interferometric spectroscopy with a single entangled photon-pair