Fig. 4: Experimental setup and experiment-theory comparisons.

A Scanning electron microscope micrograph of the central part of the fabricated sample. Subsystems A and B (cf. Fig. 1B) are highlighted by shaded blue and shaded red areas, respectively. Transport directions of edge states in the arms associated with the sources \({{{{{{{{\mathcal{S}}}}}}}}}_{A,B}\) and drains \({{{{{{{{\mathcal{D}}}}}}}}}_{A,B}\), \({\tilde{{{{{{{{\mathcal{D}}}}}}}}}}_{A,B}\), as well as in the diluted middle arms \({{{{{{{{\mathcal{M}}}}}}}}}_{A,B}\), are indicated by dashed black arrows. B, C Double-source and single-source cross-correlations (CCs), respectively [see Eq. (S48) of the Supplementary Information (SI) for expressions that include interaction contributions]. In both cases, theoretical curves with interaction taken into account (blue curves) agree better with the experimental data (black dots). D, E Measured data for the entanglement pointer (EP) and statistics-induced entanglement entropy (SEE). D Compares the measured EP (black dots) with theoretical curves: including interaction contributions (blue) and non-interacting particles (red). Although the interaction strength is the same as in (B, C), the difference between the theoretically calculated values of the EP with and without interaction contribution is much smaller than for the cross-current correlations, in panels (B, C). This demonstrates that the expression for the EP subtracts the interaction contribution to the leading order. E Comparison between the experimentally measured data (black dots) and the theoretical dependence of S_SEE on the source current (here τ_dwell = 0.01 ns as in Fig. 4). Experimental data points are obtained in two steps (see SI Sect. S1D for details): (i) we evaluate \({\tilde{S}}_{{{{{{{{\rm{SEE}}}}}}}}}\) (using Eq. (7)) with the measured EP from panel (D), and, (ii) relying on the fact that at the experimental value \({{{{{{{\mathcal{T}}}}}}}}\,=\,0.53\) the ratio \({S}_{{{{{{{{\rm{SEE}}}}}}}}}/{\tilde{S}}_{{{{{{{{\rm{SEE}}}}}}}}}\,\approx\,1.22\) in (B), we use this ratio to scale the measured \({\tilde{S}}_{{{{{{{{\rm{SEE}}}}}}}}}\) to reconstruct S_SEE. Both the interacting (blue) and non-interacting (red) theoretical curves for S_SEE agree remarkably well with the experimental data. The error bars represent the standard deviation of the mean for the set of measurements (see SI for more details).