Homodyne measurement with a Schrödinger cat state as a local oscillator

Homodyne measurements are a widely used quantum measurement. Using coherent state of large amplitude as the local oscillator, it can be shown that homodyne measurement limits to field quadrature In this work, we give an example general idea: injecting non-classical states oscillator led measurements. Specifically consider superposition states, Schr\"odinger cat state, oscillator. We derive Kraus operators and positive operator-valued measure (POVM) in situation.