Figure 3

Measured uncertainties in transmission estimation as a function of mean transmission T. The results are plotted as the product \(\langle \Delta ^{2}T \rangle \langle \hat{n}_{p} \rangle _{r}\) to make them independent of probe power or detection bandwidth used for the estimation and obtain a better comparison with the QCRB. Black and green data points correspond to the bTMSS and coherent state measurements, respectively. The vertical lines, not always visible, around each data point are the one sigma standard deviation over the 20 measurements performed at each mean transmission. The red lines are the QCRB predictions for the generated bTMSS (solid) with estimated squeezing parameter \(s=2.04\pm 0.02\) and internal source probe losses of \(T_{a}=71\%\pm 2\%\) (see Appendix A.5) and coherent state (dashed), with the shaded grey regions giving the one sigma uncertainty in the theoretical predictions to account for uncertainties in the required calibrations of \(T_{p}=97.3\%\pm 1\%\), \(\eta _{p}=94.5\%\pm 2\%\), and \(\eta _{p}=91.9\%\pm 2\%\). No free parameters or fittings were used for the QCRB plots, which take into account all the experimental imperfections that were independently calibrated. As can be seen, our measurements with bTMSS and coherent states saturate their respective QCRB.