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.

Figure 1

Teleportation scheme. Thin lines are the paths of the photons labeled by modes $a_{ni},b_{ni},c_{ni},d_{ni}$ where $n$ are spatial mode labels and $i$ are qudit labels. The qudit may be realized by time bins labeled by $i$, for example. Thick lines correspond to classical commutation channels. The parts of the apparatus in possession by Alice (the sender), Bob (the receiver), and the permutation entangled state preparation are indicated. Wiggly lines denote entanglement of the permutation entangled state. Photons start at $N$ entangled photon sources (EPS) and enter linear optical networks $V$ and $U$ and are detected. The detector results are fed forward and a local unitary operation $W$ is performed. At the end, the state on mode $a_{0i}$ is teleported to mode $a_{Ni}$.