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

TL;DR

This paper investigates the ultimate precision limits of SU(2) and SU(1,1) interferometers in noisy conditions, emphasizing the importance of the quantum Fisher information matrix over the QFI-only approach, especially under photon losses.

Contribution

It generalizes the quantum Fisher information matrix approach to noisy SU(2) and SU(1,1) interferometers, providing a more accurate precision limit analysis under photon loss noise.

Findings

Overestimated QFI disappears with increasing photon loss

QFIM approach reveals recovery phenomena in precision limits

Numerical analysis with coherent and squeezed states supports the theoretical model

Abstract

The quantum Fisher information (QFI) in SU(2) and SU(1,1) interferometers was considered, and the QFI-only calculation was overestimated. In general, the phase estimation as a two-parameter estimation problem, and the quantum Fisher information matrix (QFIM) is necessary. In this paper, we theoretically generalize 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 very usual noise may happen to the phase measurement process. Using coherent state and squeezed vacuum state as a specific example, we numerically analyze the variation of the overestimated QFI with the loss coefficient, and find its disappearance and recovery phenomenon.