Super-sensitive phase estimation with coherent boosted light using parity measurements

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach-Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer-Rao bound than the pure active (e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by CavesPhys. Rev. D 23 1693 (1981), and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves' scheme.