Fig. 4
From: Experimental benchmarking of quantum state overlap estimation strategies with photonic systems
Adaptive overlap estimation strategy based on TP and SCM. a Comparison between the TP strategy and the SCM strategy for four exemplary overlaps indicated in (c). Markers represent the experimentally estimated overlaps obtained using both strategies with \(N\,=900\) copies of the sampled qubit pair. The histograms along the horizontal (SCM) and vertical (TP) axes depict the marginal distributions of \(200\) estimated overlaps. The red dashed lines in the histograms represent the corresponding Gaussian function fittings. The black dashed line ellipse in each panel, with principal axes proportional to the standard deviations of the marginal distributions, demonstrates the relative precision of the two strategies. b Schematic of the two-step adaptive strategy for overlap estimation. In the first step, an initial estimation of overlap \({\widetilde{c}}^{{\prime} }\) is obtained using SCM with \(\alpha N\) (\(0 < \alpha < 1\)) copies of \(\left|\psi \right\rangle |\phi \rangle\). Based on the comparison between \({\widetilde{c}}^{{\prime} }\) and \({c}_{t}\), one of the TP and SCM strategies is chosen for the second step with \((1-\alpha )N\) copies of \(|\psi \rangle |\phi \rangle\). The final estimation \(\widetilde{c}\) is obtained through the maximum likelihood estimation (MLE) using the two-step overlap estimation results. c Simulation results of the adaptive strategy. \(N=900\) and \(\alpha =1/30\) are adopted in the simulation
