Ultimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution

Photon counting measurement has been regarded as the optimal measurement scheme for phase estimation in the squeezed-state interferometry, since the classical Fisher information equals to the quantum fisher information and scales as ${\overline{n}}^2$ for given input number of photons $\overline{n}$. However, it requires photon-number-resolving detectors with a large enough resolution threshold. Here we show that a collection of N-photon detection events for N up to the resolution threshold  ∼$\overline{n}$ can result in the ultimate estimation precision beyond the shot-noise limit. An analytical formula has been derived to obtain the best scaling of the fisher information. (paper)