Fig. 1. Single photon quantum state spatial-domain coding schemes. (a) Single photon path encoding; (b) OAM encoding of SPP optical element^[36]; (c) OAM encoding of q-plate optical element^[37]; (d) single photon two degrees of freedom information encoding schematic^[31]; (e) single photon three degrees of freedom encoding schematic^[32]

Fig. 2. Interferometric separation of OAM^[51]. (a) Dove prism modulation of OAM; (b) separation of OAM using BS and Dove prisms

Fig. 3. Experimental scheme of discrete quantum random walk of spatial degree of freedom^[102]. (a) Birefringent beam shifter; (b) quantum random walk of OAM degree of freedom

Fig. 4. Preparation and test of multi-dimensional maximum entangled state. (a) Three-dimensional maximum entangled state^[12]; (b) thirty-two-dimensional maximum entangled state^[28]

Fig. 5. OAM spectrum generated by conversion under spontaneous parameterization of 0th-order pump beam^[117]

Fig. 6. Interconversion of OAMs with different topological charges. (a) 3-fold increase of OAM realized by fan-out raster replication^[125]; (b) conversion of arbitrary rational factorization of OAM by logarithmic spiral transformation^[128]

Fig. 7. Experimental principles and calculations of high dimensional OAM entangled state tomography^[140]. (a) Sketch of experimental setup; (b) arbitrary dimensional OAM entangled state tomography by two projection measurements of signal photons

Fig. 8. Preparation of hyperentangled states^[174]

Fig. 9. HOM interference of hyperentangled states. (a) HOM interference curves of polarization-OAM hyperentangled Bell states^[174]; (b) exchange phase measurement of OAM Bell states^[174]

Fig. 10. Setup for generating 12-photon polarization entanglement state^[11]