  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 $\otimes$ 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
individual $N$-photon components, 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 $\bar{n}$ in the input state, over $96$ percent of
the Heisenberg limit can be achieved with the number resolution larger than
$5\bar{n}$.

Quantum Physics;Optics