  We introduce entanglement purification protocols for d-level systems (qudits)
with improved efficiency as compared to previous protocols. While we focus on
protocols for bipartite systems, we also propose generalizations to
multi-partite qudit systems. The schemes we introduce include recurrence
protocols that operate on two copies, as well as hashing protocols that operate
on large ensembles. We analyze properties of the protocols with respect to
minimal required fidelity and yield, and study their performance in the
presence of noise and imperfections. We determine error thresholds and study
the dependence on local dimension. We find that our schemes do not only
outperform previous approaches, but also show an improved robustness and better
efficiency with increasing dimension. While error thresholds for different
system sizes are not directly comparable, our results nevertheless suggest that
quantum information processing using qudits, in particular for long-distance
quantum communication, may offer an advantage over approaches based on qubit
systems.
