Optimal phase sensitivity of a lossy Mach-Zehnder interferometer with coherent and cat state inputsGarrett F. Jepson and Wenchao Ge*

A Mach-Zehnder interferometer powered by coherent light and a nonclassical state can enhance the sensitivity of estimating phase differences below the shot-noise limit.  

We study the conditions to achieve the optimal phase sensitivity of a Mach-Zehnder interferometer with coherent light and a cat state under independent photon losses in both output modes. We analytically determine a phase-matching condition (PMC) that maximizes the quantum Fisher information (QFI) for any losses. We numerically determine the optimal energy balance between the two input modes for a given total mean photon number, which is much greater than unity. Without losses, the optimal energy is balanced between the classical and nonclassical states for a large total energy; however, with losses the optimal energy balance shifts towards the classical mode. We find that quantum enhancement remains even with high losses.