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Optimal measurement scheme with an efficient data processing is important inquantum-enhanced interferometry. Here we prove that for a general binaryoutcome measurement, the simplest data processing based on inverting theaverage signal can saturate the Cram\'{e}r-Rao bound. This idea is illustratedby binary outcome homodyne detection, even-odd photon counting (i.e., paritydetection), and zero-nonzero photon counting that have achieved super-resolvedinterferometric fringe and shot-noise limited sensitivity in coherent-lightMach-Zehnder interferometer. The roles of phase diffusion are investigated inthese binary outcome measurements. We find that the diffusion degrades thefringe resolution and the achievable phase sensitivity. Our analytical resultsconfirm that the zero-nonzero counting can produce a slightly bettersensitivity than that of the parity detection, as demonstrated in a recentexperiment.

Quantum interferometry with binary-outcome measurements in the presence of phase diffusion