Quantum interferometry via a coherent state mixed with a squeezed number state

We theoretically investigate the phase sensitivity with parity measurement on a Mach-Zehnder interferometer with a coherent state combined with a squeezed number state. Within a constraint on the total mean photon number, we find, via parity measurement, that the mixing of a coherent state and squeezed number state can give better phase sensitivity than mixing a coherent state and squeezed vacuum state when the phase shift deviates from the optimal phase φ=0. In addition, we show that the classical Fisher information for parity measurement saturates the quantum Fisher information when the phase shift approaches to zero. Thus, the quantum Cramér-Rao bound can be reached via the parity measurement in the case of φ=0.