  A potential quantum internet would open up the possibility of realizing
numerous new applications, including provably secure communication. Since
losses of photons limit long-distance, direct quantum communication and
widespread quantum networks, quantum repeaters are needed. The so-called
PLOB-repeaterless bound [Pirandola et al., Nat. Commun. 8, 15043 (2017)] is a
fundamental limit on the quantum capacity of direct quantum communication.
Here, we analytically derive the quantum-repeater gain for error-corrected,
one-way quantum repeaters based on higher-dimensional qudits for two different
physical encodings: Fock and multimode qudits. We identify parameter regimes in
which such quantum repeaters can surpass the PLOB-repeaterless bound and
systematically analyze how typical parameters manifest themselves in the
quantum-repeater gain. This benchmarking provides a guideline for the
implementation of error-corrected qudit repeaters.
