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

TL;DR

This paper proposes a quantum repeater scheme utilizing GKP codes for both stationary and flying qubits, combining benefits of one-way and two-way error correction to improve long-distance quantum communication.

Contribution

It introduces a novel quantum repeater protocol using GKP codes that integrates one-way and two-way error correction schemes for enhanced performance.

Findings

Intermediate parameter regimes where the combined protocol outperforms individual schemes.

Analysis shows the protocol's effectiveness depends on specific coupling efficiencies and GKP squeezing levels.

The scheme enables encoding and QEC of qudits against transmission and memory loss.

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, occuring 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.