Quantum limit of precision for phase estimation in squeezing-enhanced interferometry with a single-mode readout

Abstract

We consider an optical interferometer with coherent light in one input and a squeezed vacuum in another. Such an interferometer is known to beat the standard quantum limit of sensitivity to the difference of phase shifts in its arms. We find the ultimate limit of precision for such an interferometer by calculating the quantum Fisher information of the mixed quantum state in one of the interferometer's outputs about the difference phase. We show that, in the vicinity of the black fringe, this information is asymptotically close to the quantum Fisher information about this phase for the two-mode readout. We conclude that the single-mode readout is optimal for phase estimation in squeezing-enhanced interferometry and allows for the Heisenberg scaling of precision. We also show that the optimal local measurement in the vicinity of the black fringe consists of amplifying the output field in a phase-sensitive way and measuring its photon number.