  While the quantum metrological advantages of performing non-Gaussian
operations on two-mode squeezed vacuum (TMSV) states have been extensively
explored, similar studies in the context of two-mode squeezed thermal (TMST)
states are severely lacking. In this paper, we explore the potential advantages
of performing non-Gaussian operations on TMST state for phase estimation using
parity detection based Mach-Zehnder interferometry. To this end, we consider
the realistic model of photon subtraction, addition, and catalysis. We first
provide a derivation of the unified Wigner function of the photon subtracted,
photon added and photon catalyzed TMST state, which to the best of our
knowledge is not available in the existing literature. This Wigner function is
then used to obtain the expression for the phase sensitivity. Our results show
that performing non-Gaussian operations on TMST states can enhance the phase
sensitivity for significant ranges of squeezing and transmissivity parameters.
We also observe that incremental advantage provided by performing these
non-Gaussian operations on the TMST state is considerably higher than that of
performing these operations on the TMSV state. Because of the probabilistic
nature of these operations, it is of utmost importance to take their success
probability into account. We identify the photon catalysis operation performed
using a high transmissivity beam splitter as the optimal non-Gaussian operation
when the success probability is taken into account. This is in contrast to the
TMSV case, where we observe photon addition to be the most optimal. These
results will be of high relevance for any future phase estimation experiments
involving TMST states. Further, the derived Wigner function of the non-Gaussian
TMST states will be useful for state characterization and its application in
various quantum information protocols.
