  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.

Quantum Physics