Phase sensitivity of lossy Mach-Zehnder interferometer via photon addition operation

Photon addition operations applied to squeezed states have been shown to significantly enhance phase sensitivity. In this study, we extend this approach by applying photon addition not only to coherent states but also within a Mach--Zehnder interferometer setup, using coherent and squeezed vacuum states as input. Both intensity-difference and homodyne detection are used to evaluate photon addition schemes, and their phase sensitivities are compared under ideal and lossy conditions, respectively. We also analyze the quantum Fisher information of these two schemes. Results show both schemes improve phase sensitivity, quantum Fisher information, and loss resistance. In particular, photon addition within the interferometer performs better. Homodyne detection outperforms intensity difference detection under photon losses. Notably, each scheme has different parameter dependencies, making them suitable for different application scenarios. When the squeezing parameter is small, photon addition employed at the coherent input with intensity difference detection can approach the Heisenberg limit in ideal conditions and can exceed the standard quantum limit in high-loss conditions. Our proposed scheme represents a valuable method for quantum precision measurements.