  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.
