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  • Open Access

Quantum repeaters based on stationary and flying Gottesman-Kitaev-Preskill qudits

Stefan Häussler* and Peter van Loock†

  • *Contact author: sthaeuss@uni-mainz.de
  • †Contact author: loock@uni-mainz.de
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Phys. Rev. Research 8, 033101 – Published 24 July, 2026

DOI: https://doi.org/10.1103/yqnw-1vkc

Abstract

There are various approaches to long-range quantum communication based on conceptually different forms of quantum repeaters. Here, we explore a quantum repeater scheme that employs quantum error correction (QEC) both on the flying (light) qubits and on the stationary (matter) qubits. The idea is to combine the benefits of encoded one-way and two-way schemes where effective channel transmission and loss scaling are enhanced by means of photon loss codes and encoded quantum memories, respectively, while sacrificing some of their advantages, such as high clock rates, independent of classical communication times (one-way), and potentially large segment lengths (two-way). More specifically, we illustrate, propose, and analyze such a quantum repeater using the bosonic Gottesman-Kitaev-Preskill (GKP) code, which naturally enables encoding and QEC of qudits, protecting them against transmission and memory loss, the latter, for instance, occurring on collective spin modes of atomic ensembles. While the encoded one-way and two-way schemes on their own either require very high repeater link coupling efficiencies and GKP squeezing or allow for experimentally more feasible, small values of these parameters, respectively, we find that there are intermediate parameter regimes where the combined repeater protocol is superior.

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Phys. Rev. Research 8, 033101– Published 24 July, 2026
  • Received 8 September 2025
  • Accepted 12 June 2026
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