Fig. 5 | Nature Communications

Fig. 5

From: Experimental optical phase measurement approaching the exact Heisenberg limit

Fig. 5

Probability distribution of measurement outcomes. The probabilities of obtaining the four possible \(\{ {\mathrm{dd}},\,{\mathrm{ad}},\,{\mathrm{da}},\,{\mathrm{aa}}\}\) measurement outcomes which correspond to four possible \(\phi _{{\mathrm{est}}}\) values, for each phase value shown in Fig. 4. The variance \(V_{\mathrm{H}}^\phi\) is minimised for those ϕ values when one of the probabilities is maximum. Dots are experimental values and lines are numerical simulations that use the experimentally generated \(\rho _{{\mathrm{exp}}}\) as input. Error bars, representing the statistical uncertainty due to the finite number of measurement sets, are smaller than the dot size

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