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Teleporting photonic qudits using multimode quantum scissors

Teleportation plays an important role in the communication of quantum information between the nodes of a quantum network and is viewed as an essential ingredient for long-distance Quantum Cryptography. We describe a method to teleport the quantum information carried by a photon in a superposition of a number $d$ of light modes (a "qudit") by the help of $d$ additional photons based on transcription. A qudit encoded into a single excitation of $d$ light modes (in our case Laguerre-Gauss modes which carry orbital angular momentum) is transcribed to $d$ single-rail photonic qubits, which are spatially separated. Each single-rail qubit consists of a superposition of vacuum and a single photon in each one of the modes. After successful teleportation of each of the $d$ single-rail qubits by means of "quantum scissors" they are converted back into a qudit carried by a single photon which completes the teleportation scheme.