Phase estimation at the quantum Cramér-Rao bound via parity detection

Abstract

We show that, in two-path optical interferometry, the measurement of photon number parity achieves maximal phase sensitivity at the quantum Cram\'er-Rao bound for a certain type of path-symmetric states. All pure states of light proposed for sub--shot-noise phase sensitivity thus far in the literature are of the form of these path-symmetric states. Thus, parity measurement presents an optimal detection strategy for all of them. Our scheme is applicable for local phase estimation.