Approaching the optimal phase estimation sensitivity of the lossy Mach-Zehnder interferometer with coincidence measurements

How to find the specific measurement scheme to approach the quantum Cram & eacute;r-Rao bound (QCRB) is an important issue in quantum metrology, especially for the continuous-variable optical interferometers input with non-classical states. In the ideal situation (i.e., without any photon loss), this can be usually achieved by using the parity measurement, which, however, does not work well when the photon loss occur. Alternatively, in this work we find that the coincidence measurements are more robust to the photon loss than the parity measurement. Importantly, in certain cases, the sensitivity with the coincidence measurement can even approach very closely to the QCRB despite of the photon loss. Though the results are obtained based on the analysis with the typical two-photon twin-Fock state, it might be also generalized for the other input ones. Thus, our work may provide an effective measurement scheme for beating the shot-noise limit in practical experiments.