Performing homodyne detection at a single output port of a squeezed-state light interferometer and then separating the measurement quadrature into several bins can realize superresolving and supersensitive phase measurements. However, the phase resolution and the achievable phase sensitivity depend on the bin size that is adopted in the data processing. By maximizing classical Fisher information, we analytically derive an optimal value of the bin size and the associated best sensitivity for the case of three bins, which can be regarded as a three-outcome measurement. Our results indicate that both the resolution and the achievable sensitivity are better than that of the previous binary–outcome case. Finally, we present an approximate maximum Likelihood estimator to asymptotically saturate the ultimate lower bound of the phase sensitivity.
Data processing over single-port homodyne detection to realize superresolution and supersensitivity