  Generating entanglement between distributed network nodes is a prerequisite
for the quantum internet. Entanglement distribution protocols based on
high-dimensional photonic qudits enable the simultaneous generation of multiple
entangled pairs, which can significantly reduce the required coherence time of
the qubit registers. However, current schemes require fast optical switching,
which is experimentally challenging. In addition, the higher degree of error
correlation between the generated entangled pairs in qudit protocols compared
to qubit protocols has not been studied in detail. We propose a qudit-mediated
entangling protocol that completely circumvents the need for optical switches,
making it more accessible for current experimental systems. Furthermore, we
quantify the amount of error correlation between the simultaneously generated
entangled pairs and analyze the effect on entanglement purification algorithms
and teleportation-based quantum error correction. We find that optimized
purification schemes can efficiently correct the correlated errors, while the
quantum error correction codes studied here perform worse than for uncorrelated
error models.
