Nonlinear protocol for high-dimensional quantum teleportation

Bell measurements, which allow entanglement between uncorrelated distant particles, play a central role in quantum communication. Indeed, sharing, measuring, and creating entanglement lie at the core of various protocols, such as entanglement swapping and quantum teleportation. While for optical qubit systems a Bell measurement can be implemented using only linear components, the same result is no longer true for highdimensional states, where one has to consider either auxiliary photons or nonlinear processes. Here, inspired by the latter approach, we propose a protocol for high-dimensional quantum teleportation based on nonlinear techniques. Moreover, we discuss the practical implementation of our proposed setup in the case of path-encoded qutrits, where nonlinear effects arise from sum-frequency generation. Finally, we compute the fidelity between quantum states to benchmark the validity of our model under the presence of crosstalk noise. Our approach is deterministic, versatile, and does not rely on the use of auxiliary photons, thus paving the way towards the practical implementation of quantum networks based on nonlinear effects.