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The quantum Fisher information (QFI) in SU(2) and SU(1,1) interferometers wasconsidered, and the QFI-only calculation was overestimated. In general, thephase estimation as a two-parameter estimation problem, and the quantum Fisherinformation matrix (QFIM) is necessary. In this paper, we theoreticallygeneralize the model developed by Escher et al [Nature Physics 7, 406 (2011)]to the QFIM case with noise and study the ultimate precision limits of SU(2)and SU(1,1) interferometers with photon losses because photon losses as a veryusual noise may happen to the phase measurement process. Using coherent stateand squeezed vacuum state as a specific example, we numerically analyze thevariation of the overestimated QFI with the loss coefficient, and find itsdisappearance and recovery phenomenon.

Ultimate precision limit of SU(2) and SU(1,1) interferometers in noisy metrology