# Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters

## TL;DR

This paper analytically derives the gain of error-corrected qudit quantum repeaters and identifies parameter regimes where they can surpass the fundamental PLOB bound, guiding future quantum network implementations.

## Contribution

It introduces a systematic analysis of error-corrected qudit repeaters, identifying conditions to exceed the PLOB bound with two physical encodings.

## Key findings

- Quantum repeaters can surpass the PLOB bound under specific parameters.
- Error-corrected qudit repeaters are effective for long-distance quantum communication.
- Benchmarking guides practical implementation of qudit-based quantum repeaters.

## Abstract

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.