<p>We investigate the role of local Gaussian operations, specifically local displacement operations (LDOs) and local squeezing operations (LSOs), in enhancing the phase sensitivity of a Mach–Zehnder interferometer (MZI). We consider both single-arm and dual-arm implementations of these operations and analyze the resulting phase sensitivity and quantum Cramér–Rao bound (QCRB) using coherent and squeezed vacuum inputs under homodyne detection, for both ideal and lossy conditions. We show that, under appropriate assumptions on the displacement parameters, single-arm and dual-arm LDO schemes yield identical phase sensitivity, indicating that a single-arm implementation is sufficient for displacement-assisted enhancement. In contrast, for local squeezing operations, the dual-arm LSO scheme consistently outperforms its single-arm counterpart under corresponding assumptions on the squeezing parameters. We further demonstrate that both LDO and LSO schemes improve robustness against photon loss and lead to a reduced QCRB in both ideal and lossy scenarios. Our results highlight local Gaussian operations as experimentally feasible, low-cost tools for enhancing phase sensitivity and loss robustness in quantum optical interferometry, within the considered framework.</p>