Quantum interferometry via a coherent state mixed with a squeezed number state**Project supported by the National Natural Science Foundation of China (Grant No. 11404040) and the Qing Lan Project of the Higher Educations of Jiangsu Province of China.

Abstract

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.