Fig. 2.

Experimental evidence demonstrating rapid convergence under finite sample size with favorable constant factors. a Mean fidelity estimates from 30 randomly sampled subsets of Pauli matrices as a function of the size $K$ of the subset. The error bars illustrate the standard deviation of the 30 samples, that is, the standard error of the mean. The green line describes the mean fidelity $F=97.25\left(8\right)$% calculated from the complete data set. b The standard deviation of the fidelity from plot a against $K$ including a bound due to finite sampling of Pauli channels ${\sigma }_{\mathrm{Pauli}}=0.0275\left(8\right)∕\sqrt{K}$ in orange, a fit of the standard deviation $\sigma =0.0127\left(2\right)∕\sqrt{K}$ in green, and a fit of the expected projection noise ${\sigma }_{\mathrm{lower}}=0.00375\left(1\right)\sqrt{K}$ in red (see Supplementary Note 5).