Fig. 3: Simulation analyses.
From: Ultra-high dynamic range quantum measurement retaining its sensitivity
a For different relative numbers of iterations of the subsequences (written directly left of each curve) of areas A, the uncertainty σB with respect to measurement time Tmeas changes. Depending on the measurement time, a different combination gives the lowest uncertainty. b Minimised uncertainty for a large-range sequence by optimally combining the subsequences (red line). The dashed lines give the uncertainty for single-area sequences (A0 blue, A0/2 magenta, A0/4 olive, A0/8 grey). See Supplementary Note 1 for maximum uncertainty ∝ range. c The relative number of iterations for each area (A0 blue crosses, A0/2 magenta circles, A0/4 olive triangles, A0/8 grey diamonds kept at 100) for each measurement time to minimise the uncertainty, which results in the red line in b. The vertical arrows indicate when a subsequence for its area turns on, since its relative number of iterations becomes significant. The green dashed line gives the relative difference between the most-sensitive small-range sequence (blue dashed line in b) compared to the optimally combined large-range sequence. This difference scales inversely with the measurement time. d When looking at the turning-on points (yellow crosses, fit with black dotted line) for many sequences with different areas (largest area blue line, smallest area red line), it scales as \({T}_{{\rm{meas}}}^{-2}\) for short measurement times. Please note that the optimally combined result in b scales as \({T}_{{\rm{meas}}}^{-0.98}\), since it includes relatively large areas only, equivalent to the lowest lines in this plot.
