  Absorption and gain processes are fundamental to any light-matter interaction
and a precise measurement of these parameters is important for various
scientific and technological applications. Quantum probes, specifically the
squeezed states have proved very successful, particularly in the applications
that deal with phase shift and force measurements. In this paper, we focus on
improving the sensitivity of the estimation of the photon loss coefficient of a
weakly absorbing medium as well as the estimation of the gain parameter using a
two-mode bright squeezed state. The generation of this state combines the
advantage of a coherent beam for its large photon number with the quantum
properties of the two-mode squeezing operation in an optical parametric
amplifier. We present two measurement schemes: balanced photodetection and
time-reversed metrology, both utilizing two-mode bright squeezed light. The
maximum quantum advantage we can achieve using two-mode bright squeezed light
is 3.7 times for the absorption parameter $\alpha = 0.05$ and 8.4 times for
$\alpha = 0.01$ as compared to using only the coherent state. Similarly, the
maximum quantum advantage for the estimation of optical gain is found around
2.81 times for the gain coefficient $G=1.05$ and around 6.28 times for
$G=1.01$. We discuss the significance of using one measurement scheme over the
other under different squeezing conditions. We compare our results with the
Cram\'er-Rao bound for a two-mode bright squeezed state to assess the quality
of the proposed methodologies.
