Fig. 2: The weak gain regime.
From: Quantum-enhanced interferometry with large heralded photon-number states
a Rates measured with the probe \(\left|1,1\right\rangle\): (s1, s2, h1, h2) = (2, 0, 1, 1) [blue], (1, 1, 1, 1) [orange], (0, 2, 1, 1) [green]. b Rates measured with the probe \(\left|2,1\right\rangle\): (3, 0, 2, 1) [blue], (2, 1, 2, 1) [orange], (1, 2, 2, 1) [green], (0, 3, 2, 1) [red]. Error bars are one standard deviation assuming Poissonian counting statistics. Lines are a model fitted to \({{\rm{pr}}}_{{s}_{1},{s}_{2},{h}_{1},{h}_{2}}(\phi )\). Bottom panels show the normalized Fisher information \({\tilde{{\mathcal{F}}}}_{{h}_{1},{h}_{2}}(\phi )\) calculated using two methods: (i) post-selecting on events where s1 + s2 = h1 + h2 [green] and (ii) using all events [red]. Line thicknesses show 1σ confidence intervals obtained by fitting 50 simulated data sets that are calculated with a Monte Carlo method. The dashed black line indicates the shot-noise limit.
