Fig. 4 | Nature Communications

Fig. 4

From: Experimental optical phase measurement approaching the exact Heisenberg limit

Fig. 4

Heisenberg-limited phase estimation with N = 3 resources. Red dots represent experimentally measured variance \(V_{\mathrm{H}}^\phi\) as a function of ϕ. The red horizontal line-segment cutting the left axis shows the optimal protocol Holevo variance \(V_{\mathrm{H}} = 0.5497 \pm 0.0007\), determined from these data, while blue line-segment shows the HL. The blue and the green curves represent results of numerical simulations of the variance for the ideal optimal state \(\rho _{{\mathrm{opt}}}\) and experimentally prepared state \(\rho _{{\mathrm{exp}}}\), respectively. Brown dots represent \(V_{\mathrm{H}}^\phi\) for the shot-noise-limited interferometry and the black dashed line represents the measured Holevo variance \(V_{\mathrm{H}} = 0.7870 \pm 0.0007\) for the same measurement. The grey solid line shows the SNL. Numerical values for the experimental results and corresponding limits are detailed in Table 2. Each data point was calculated from at least 50,000 twofold coincidence events and the error bars represent 95% confidence intervals calculated with the bootstrap method23

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