Realistic non-Gaussian operations scheme in parity detection based Mach-Zehnder quantum interferometry

We theoretically analyze phase sensitivity using parity detection based Mach Zehnder interferometer (MZI) with the input states generated by performing non-Gaussian operations, viz., photon subtraction, photon addition, and photon catalysis on a two-mode squeezed vacuum (TMSV) state. Since these non-Gaussian operations are probabilistic, it is of utmost importance to take the success probability into account. To this end, we consider the realistic model of photon subtraction, addition, and catalysis and derive a single expression of the Wigner function for photon subtracted, added, and catalyzed TMSV state. The Wigner function is used to evaluate the lower bound on the phase sensitivity via quantum Cramer-Rao bound and parity detection based phase sensitivity in MZI. We identify the ranges of squeezing and transmissivity parameters where the non-Gaussian states provide better phase sensitivity than the TMSV state. On qualitatively taking the success probability into account, it turns out that the photon addition is the most advantageous non-Gaussian operation. We hope that the generalized Wigner function derived in this work will be useful in various quantum information protocols and state characterization.