Phase-Matching Condition for Superpositions of Coherent States in a Mach-Zehnder Interferometer

We discussed the phase-matching condition of the input states for a specific Mach-Zehnder interferometer to enhance the phase sensitivity. The input states are a coherent state and a superposition of coherent states. For both cases with and without photon losses, the phase-matching condition to enhance phase sensitivity is found to be unchanged no matter the input state has parity or not.