Fig. 3: Measured weak values of the diagonal polarization (X) and spatial (Y) degrees of freedom.
The coincidence distribution (photon detected in coincidence with the corresponding heralded photon) of the photons for Xw is shown on the X axis through the red histogram plot. The mean and 1σ errors from the distribution are shown above the histogram while the values are mentioned alongside the box. Similarly, the distribution for Yw is shown along the Y-axis through the blue histogram plot. Since both the pointer shifts occur concurrently and are measured jointly in the experiment (i.e., without changing anything between pre and post-selection), the overall shift of the pointer is along the diagonal, as inferred from the shifts on the projections along horizontal X and vertical Y. The distribution of these diagonal shifts, in terms of the weak values, is represented by the scatter plots. The pink and light blue bands represent the systematic error bands for the coincidence measurements (±0.070 for Xw and ±0.095 for Yw, respectively). As can be seen, both measured weak values (0.890 ± 0.093) for Xw (the diagonal component of the polarization DOF) and (1.080 ± 0.134) for Yw (the spatial DOF) lie well within the systematic error band of the experiment. Details of the error analysis are given in the Methods section.
