Sketch of the setup to generate hybrid entanglement between polarization and high-OAM quanta. (A) First, polarization entanglement is created (gray box), then one photon is transferred to high-OAM quanta in a Michelson-type interferometric scheme (blue box and inset) depending on the polarization. The transfer to ±500 and ±1,000 quanta of OAM is done directly from Gaussian modes by SPMs. For the highest quantum number we first transferred photons to ±10 (red dashed box) (11) before sending them into the transfer setup with SPMs for 10,000ħ, and thus we generate modes with ±10,010 quanta of OAM per photon. The transfer is completed by projecting on diagonal polarization with a polarizer after the setup. (B) Alice: The polarization state of unchanged photon is measured with a combination of half and quarter wave plates (HWP and QWP), a polarizing beam splitter (PBS), and APDs. (C) Bob: If the photon is transferred to ±500ħ, we demonstrate entanglement by coincidence imaging, where an ICCD is triggered depending on the polarization measurement of Alice (27). If the photons are transferred to ±1,000ħ and 10,010ħ, we test entanglement by measuring correlations (logic) between the polarization measurements of Alice and OAM superposition measurements, realized by appropriate masking in front of a bucket detector (APD), of Bob.