Figure 3: Experimental data showing the direct measurement of a rotated high-dimensional state vector.

The created state is rotated by angles θ_±=±π/9 rad (insets of (b,e)). (a,d) The measured real (blue circles) and imaginary parts (red triangles) of the rotated state vectors. (b,e) The calculated probability densities . (c,f) The phase difference φ_±() between the calculated phase and the phase of the unrotated case from Fig. 2c. Theoretical fits to the probability densities and phases are plotted as blue lines. The linear fits in (c,f) are calculated via the process of χ² minimization, which takes into account the error at each point. Error bars are calculated by propagating the detector error (due to background light and dark counts) through to all measured quantities. Error bars larger than the symbols are shown. The data shown are the average result obtained from 50 experimental runs.