Advantage of Non‐Gaussian Operations in Phase Estimation via Mach–Zehnder Interferometer

Abstract This study investigates the benefits of probabilistic non‐Gaussian operations in phase estimation using difference‐intensity and parity detection‐based Mach–Zehnder interferometers (MZI). An experimentally implementable model is considered 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. The findings reveal that all non‐Gaussian operations except one PC operation provide an advantage in either of the measurement schemes. This result is further supported by the analysis of the quantum Cramér–Rao bound. When accounting for the success probability of non‐Gaussian operations, two‐PC and four‐PA emerges as the most optimal operations in difference‐intensity and parity detection‐based MZI, respectively. Additionally, the corresponding squeezing and transmissivity parameters that yields the best performance are identified, making the study relevant for experimentalists. Furthermore, a general expression for the moment‐generating function is derived, which is useful in exploring other detection schemes such as homodyne detection and quadratic homodyne detection.