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Quantum teleportation allows protected information exchange between distant parties without the need for a physical link, a crucial re- source in future quantum networks. Using high-dimensional quantum states for teleportation offers the promise of higher information capacity channels, protection against optimal cloning machines and improved resilience to noise, but is limited by the commonly used linear optical detection requiring ancillary photons, where the number of entangled photons grows with the dimension to be teleported. Here we overcome this restriction with non-linear optical detection and demonstrate the teleportation of high-dimensional states with just two entangled photons as a quantum resource . Using photonic spatial modes as an example, we demonstrate a 15-dimensional teleportation channel, exceeding the state-of-the-art of three dimensions, offering a scaleable route to high-capacity quantum information transfer.
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