Fig. 2: Reconstruction fidelity.

For each basis size, we compare the process tensor predictions with experimentally reconstructed density matrices for predictions that lay outside the basis set. a The average infidelity in reconstruction between the states predicted by the process tensor and the experimentally measured state. This includes a 95% confidence interval, computed using the bootstrapping method described in ref. ⁴¹. The experiments compare the predictions of a basis n process tensor with the experimental outcomes of the 4 × (28 − n) × (28 − n) experiments from outside the basis set. In the notation of the ‘Process characterisation’ subsection, our basis is \({\mathcal{P}}\otimes {{\mathcal{U}}}^{(n)}\otimes {{\mathcal{U}}}^{(n)}\). b The distribution of fidelities of the predictions made by a basis-24 process tensor over a range of experiments. The top and bottom of the boxes are, respectively, the 25th and 75th percentiles, the whiskers are 1.5 times the inter-quartile range, and the orange lines are the medians of the distribution, with this last figure also provided in orange to four decimal places.