Rate-distance tradeoff and resource costs for all-optical quantum repeaters

TLDR

The paper presents a resource‑performance tradeoff for an all‑optical quantum repeater that uses photon sources, linear optics, photon detectors, and classical feedforward but no quantum memories, and proposes protocol modifications that reduce the required photon sources per node from ~10¹¹ to ~10⁶. The authors analyze a repeater architecture based on photon sources, linear optics, detectors, and feedforward, and show how to lower the photon‑source count needed to generate photonic clusters at each node. They find that the secure key rate follows R(η)=Dη^s with s<1 achievable even with lossy devices, allowing the repeater to outperform direct transmission (R_direct≈(1/ln 2)η) beyond a certain range, and that the optimal repeater spacing is about 1.5 km regardless of total distance.

Abstract

We present a resource-performance tradeoff of an all-optical quantum repeater that uses photon sources, linear optics, photon detectors and classical feedforward at each repeater node, but no quantum memories. We show that the quantum-secure key rate has the form $R(\eta) = D\eta^s$ bits per mode, where $\eta$ is the end-to-end channel's transmissivity, and the constants $D$ and $s$ are functions of various device inefficiencies and the resource constraint, such as the number of available photon sources at each repeater node. Even with lossy devices, we show that it is possible to attain $s < 1$, and in turn outperform the maximum key rate attainable without quantum repeaters, $R_{\rm direct}(\eta) = -\log_2(1-\eta) \approx (1/\ln 2)\eta$ bits per mode for $\eta \ll 1$, beyond a certain total range $L$, where $\eta \sim e^{-\alpha L}$ in optical fiber. We also propose a suite of modifications to a recently-proposed all-optical repeater protocol that ours builds upon, which lower the number of photon sources required to create photonic clusters at the repeaters so as to outperform $R_{\rm direct}(\eta)$, from $\sim 10^{11}$ to $\sim 10^{6}$ photon sources per repeater node. We show that the optimum separation between repeater nodes is independent of the total range $L$, and is around $1.5$ km for assumptions we make on various device losses.