  We investigate the benefits of probabilistic non-Gaussian operations in phase
estimation using difference-intensity and parity detection-based Mach-Zehnder
interferometers (MZI). We consider an experimentally implementable model to
perform three different non-Gaussian operations, namely photon subtraction
(PS), photon addition (PA), and photon catalysis (PC) on a single-mode squeezed
vacuum (SSV) state. In difference-intensity detection-based MZI, two PC
operation is found to be the most optimal, while for parity detection-based
MZI, two PA operation emerges as the most optimal process. We have also
provided the corresponding squeezing and transmissivity parameters at best
performance, making our study relevant for experimentalists. Further, we have
derived the general expression of moment-generating function, which shall be
useful in exploring other detection schemes such as homodyne detection and
quadratic homodyne detection.
