Figure 1

An interferometric scheme with coherent and squeezed vacuum states interfered at a beam-splitter, with arbitrary quantum measurement potentially involving an additional reference beam. In general, the QFI bounds on the phase-estimation precision depend on the way the interferometer phase delay is modeled: (i) phase shift only in the upper arm, (ii) phase shift distributed symmetrically, (iii) phase shifts defined with respect to an additional reference beam.Reuse & Permissions

Figure 2

Bounds on the phase estimation precision calculated using the QFI, in the cases of ideal (black) and lossy ($\eta =0.8$, gray) interferometers. Different curves correspond to QFI calculated using different models: $F_Q^{\left(i\right)}$ (dotted), $F_Q^{\left(ii\right)}$ (dashed), $F_Q^{\left(\rho \right)}$ (solid). In the case of a lossy interferometer, the additional reference beam may improve the precision: ${\left({\mathcal{F}}^{-1}\right)}_{--}\text{(gray,}\text{solid,}\text{bottom)}<{\left(F_Q^{\left(\rho \right)}\right)}^{-1}\text{(gray,}\text{solid,}\text{top)}$, while for the ideal interferometer these quantities coincide.Reuse & Permissions