Recognition of Light Orbital-Angular-Momentum Superpositions for Quantum Communication

We study the tomography of spatial qudits encoded on structured light photons in the space of fixed order transverse modes. While direct position measurements with cameras do not provide an informationally complete Positive Operator Valued Measure (POVM), this property is achieved with the use of astigmatic transformation, allowing full characterization of the spatial quantum state from simple intensity measurements in both the intense and in the low photocount regimes. These methods are useful for classical and quantum communication with structured light and will be tested in a quantum network being set up in the Rio de Janeiro metropolitan area.