Quantum teleportation of photonic qudits using linear optics

One of the challenges of photon-based quantum teleportation is that both a source of entangled photons and an entangled basis measurement are required. For qubits, one can perform a probabilistic entangled basis measurement using linear optics, making the scheme efficient. However, for photonic qudits, an equivalent scheme remains difficult to devise. In this paper, we generalize the probabilistic photonic qubit teleportation protocol to qudits. The method relies on producing permutation entangled states nondeterministically which are superpositions of permutations of the spatial and qudit states of the photons. Our scheme nondeterministically teleports a photonic qudit using only entangled photon sources, linear optics, and photon detectors, and should be experimentally realizable for small qudit dimensions.