  It depends. For a single molecule interacting with one mode of a biphoton
probe, we show that the spectroscopic information has three contributions, only
one of which is a genuine two-photon contribution. When all the scattered light
can be measured, solely this contribution exists and can be fully extracted
using unentangled measurements. Furthermore, this two-photon contribution can,
in principle, be matched by an optimised but unentangled single-photon probe.
When the matter system spontaneously emits into inaccessible modes, an
advantage due to entanglement can not be ruled out. In practice, time-frequency
entanglement does enhance spectroscopic performance of the oft-studied
weakly-pumped spontaneous parametric down conversion (PDC) probes. For
two-level systems and coupled dimers, more entangled PDC probes yield more
spectroscopic information, even in the presence of emission into inaccessible
modes. Moreover, simple, unentangled measurements can capture between 60% - 90%
of the spectroscopic information. We thus establish that biphoton spectroscopy
using source-engineered PDC probes and unentangled measurements can provide
tangible quantum enhancement. Our work underscores the intricate role of
entanglement in single-molecule spectroscopy using quantum light.
