  Optimal measurement scheme with an efficient data processing is important in
quantum-enhanced interferometry. Here we prove that for a general binary
outcome measurement, the simplest data processing based on inverting the
average signal can saturate the Cram\'{e}r-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.
