Fisher information of a squeezed-state interferometer with a finite photon-number resolution

Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the output ports. Here we show that for each individual N-photon component of the phase-matched coherent circle times squeezed vacuum input state, the classical Fisher information always saturates the quantum Fisher information. Moreover, the total Fisher information is the sum of the contributions from each individualN- photon component, where the largest N is limited by the finite number resolution of available photon counters. Based on this observation, we provide an approximate analytical formula that quantifies the amount of lost information due to the finite photon number resolution; e.g., given the mean photon number (n) over bar in the input state, over 96% of the Heisenberg limit can be achieved with the number resolution larger than 5n (n) over bar.