Ab initio phase estimation at the shot noise limit with on–off measurement

Phase resolution at the shot noise limit can be achieved with coherent states and on–off measurement. However, the estimation of an unknown phase using this scheme is still missing. Here, we experimentally demonstrate an ab initio phase estimation at the shot noise limit using on–off measurement and efficient Bayesian inference algorithm. The performance of the schemes with and without real-time feedback control is compared. The scheme with feedback control eliminates the ambiguity in the phase estimation and accelerates the convergence to true value. The shot noise limit that defines the ultimate precision is saturated independent of the true phase after about 150 rounds of measurement and feedback control. Our protocol may find important applications in practical precision metrology when only a limited number of measurements are allowed.