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

TL;DR

This paper analyzes the resource and performance tradeoffs in all-optical quantum repeaters without quantum memories, demonstrating how to surpass direct transmission rates with optimized resource allocation and repeater spacing.

Contribution

It introduces a resource-performance model for all-optical quantum repeaters, showing how to outperform direct transmission rates with fewer photon sources and optimized node spacing.

Findings

Quantum-secure key rate scales as R(η) = Dη^s with device inefficiencies.

Achieves outperforming direct transmission rate beyond a certain fiber length.

Reduces photon source requirements from 10^11 to 10^6 per repeater node.

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.