Optimal binary strategy for angular displacement estimation based upon fidelity appraisal

We report on an optimal binary strategy for angular displacement estimation. The measuring system is a modified Mach-Zehnder interferometer fed by a coherent state carrying orbital angular momentum, and two Dove prisms are embedded in two paths. In terms of the fidelity appraisal, parity detection and Z detection are discussed, and the optimal estimation strategy is presented. We additionally study the effects of several realistic scenarios on the fidelity, including transmission loss, detection efficiency, dark counts, and those which are a combination thereof. Finally, we exhibit a proof of principle experiment and perform Bayesian estimation on data processing. The experimental results imply resolved enhancement by a factor of 1.86 suggesting super-resolving signal. Meanwhile, on the trial greater than 500, we show that the angular displacement can be precisely estimated via acquired outcome information.