Time-domain interferometry (TDI) is a method to probe space-time correlations among particles in condensed matter systems. Applying TDI to quantum systems raises the general question, whether two-time correlations can be reliably measured without adverse impact of the measurement backaction onto the dynamics of the system. Here, we show that a recently developed quantum version of TDI (QTDI) indeed can access the full quantum-mechanical two-time correlations without backaction. We further generalize QTDI to weak classical continuous-mode coherent input states, alleviating the need for single-photon input fields. Finally, we interpret our results by splitting the space-time correlations into two parts. While the first one is associated to projective measurements and thus insensitive to backaction, we identify the second contribution as arising from the coherence properties of the state of the probed target system, such that it is perturbed or even destroyed by measurements on the system.
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