  Two-photon absorption (TPA) is of fundamental importance in super-resolution
imaging and spectroscopy. Its nonlinear character allows for the prospect of
using quantum resources, such as entanglement, to improve measurement precision
or to gain new information on, e.g., ultrafast molecular dynamics. Here, we
establish the metrological properties of nonclassical squeezed light sources
for precision measurements of TPA cross sections. We find that there is no
fundamental limit for the precision achievable with squeezed states in the
limit of very small cross sections. Considering the most relevant measurement
strategies -- namely photon counting and quadrature measurements -- we
determine the quantum advantage provided by squeezed states as compared to
coherent states. We find that squeezed states outperform the precision
achievable by coherent states when performing quadrature measurements, which
provide improved scaling of the Fisher information with respect to the mean
photon number $\sim n^4$. Due to the interplay of the incoherent nature and the
nonlinearity of the TPA process, unusual scaling can also be obtained with
coherent states, which feature a $\sim n^3$ scaling in both quadrature and
photon-counting measurements.
