Fig. 11. OAM entanglement.

a OAM entanglement is generated via Spontaneous Parametric Downconversion (SPDC) in a nonlinear crystal, where the OAM of the two SPDC photons, adding to that of the pump, l_pump = l_A + l_B, e.g., if the pump has zero OAM, then if l_A = 1 corresponds to l_B = −1, and so on, as shown in the insets. This process results in an infinite superposition state, represented by $∣\mathrm{\Psi }⟩$. b Measurement process involves a quantum version of the previously discussed modal decomposition method, typically employing holograms encoded onto SLMs, with the resulting light coupled into single-mode fibers, and the outcomes are then measured in coincidence using a coincidence counter. For OAM measurements, the holograms correspond to the standard azimuthal phases, as depicted in the insets. c Experimental validation confirms that OAM naturally forms a Schmidt basis, thereby verifying the conservation of OAM at the single-photon level