Figure 2: Experimental data showing direct measurement of a 27-dimensional state vector in the OAM basis.

The state is created by sending photons through an angular aperture of width Δθ=2π/9 rad (inset of (b)). (a) The measured real (blue circles) and imaginary parts (red triangles) of the state vector, (b) the calculated probability density , and (c) the calculated phase φ() are plotted as functions of the OAM quantum number up to a dimensionality of =±13. The probability density has a sinc-squared shape. The phase has an asymmetric quadratic shape due to small misalignments in our optical system. Additionally, π-phase jumps are seen in the phase when the probability amplitude changes sign (not seen in the probability density). Theoretical fits to the probability density and phase are plotted as blue lines. 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.