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While the quantum metrological advantages of performing non-Gaussianoperations on two-mode squeezed vacuum (TMSV) states have been extensivelyexplored, similar studies in the context of two-mode squeezed thermal (TMST)states are severely lacking. In this paper, we explore the potential advantagesof performing non-Gaussian operations on TMST state for phase estimation usingparity detection based Mach-Zehnder interferometry. To this end, we considerthe realistic model of photon subtraction, addition, and catalysis. We firstprovide a derivation of the unified Wigner function of the photon subtracted,photon added and photon catalyzed TMST state, which to the best of ourknowledge is not available in the existing literature. This Wigner function isthen used to obtain the expression for the phase sensitivity. Our results showthat performing non-Gaussian operations on TMST states can enhance the phasesensitivity for significant ranges of squeezing and transmissivity parameters.We also observe that incremental advantage provided by performing thesenon-Gaussian operations on the TMST state is considerably higher than that ofperforming these operations on the TMSV state. Because of the probabilisticnature of these operations, it is of utmost importance to take their successprobability into account. We identify the photon catalysis operation performedusing a high transmissivity beam splitter as the optimal non-Gaussian operationwhen the success probability is taken into account. This is in contrast to theTMSV case, where we observe photon addition to be the most optimal. Theseresults will be of high relevance for any future phase estimation experimentsinvolving TMST states. Further, the derived Wigner function of the non-GaussianTMST states will be useful for state characterization and its application invarious quantum information protocols.

Enhanced phase estimation in parity detection based Mach-Zehnder interferometer using non-Gaussian two-mode squeezed thermal input state