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

Optimal measurement scheme with an efficient data processing is important in quantum-enhanced interferometry. Herewe prove that for a general binary-outcome measurement, the simplest data processing based on inverting the average signal can saturate the Cramer-Rao bound. This idea is illustrated by binary-outcome homodyne detection, even-odd photon counting (i.e., parity detection), and zero-nonzero photon counting that have achieved super-resolved interferometric fringe and shot-noise limited sensitivity in coherent-light Mach-Zehnder interferometer. The roles of phase diffusion are investigated in these binary-outcome measurements. We find that the diffusion degrades the fringe resolution and the achievable phase sensitivity. Our analytical results confirm that the zero-nonzero counting can produce a slightly better sensitivity than that of the parity detection, as demonstrated in a recent experiment.