  This study explores a detailed examination of various classes of single- and
two-mode Gaussian states as key elements for an estimation process,
specifically targeting the evaluation of an unknown squeezing parameter encoded
in one mode. To quantify the efficacy of each probe, we employ the concept of
Average Quantum Fisher Information (AvQFI) as a robust metric to quantify the
optimal performance associated with specific classes of Gaussian states as
input. For single-mode probes, we identify pure squeezed single-mode states as
the optimal choice and we explore the correlation between Coherence and AvQFI.
Also, we show that pure two-mode squeezed states exhibit behavior resembling
their single-mode counterparts for estimating the encoded squeezing parameter,
and we studied the interplay between entanglement and AvQFI. This paper
presents both analytical and numerical results that encompass all the studied
classes, offering valuable insights for quantum estimation processes.
