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 (n) over bar (2) for given input number of photons (n) over bar. 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 similar to(n) over bar 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.