Rate-loss analysis of an efficient quantum repeater architecture

TLDR

The study aims to enable formal rate‑loss analyses of other repeater protocols and to supply abstractions for quantum network topologies. The authors model an entanglement‑based QKD repeater chain using photon‑pair sources, spectral multiplexing, linear‑optical Bell‑state measurements, multimode memories, and classical error correction, and analytically compute the end‑to‑end noisy state, its fidelity, entanglement‑distillation rate, and extend the analysis to non‑ideal two‑pair emission via exact numerical evaluation. They derive an exact secret‑key‑rate expression for perfect sources, show how errors propagate with loss and noise, and prove that the protocol exceeds the Takeoka‑Guha‑Wilde bound, providing a rigorous demonstration of repeater efficacy.

Abstract

We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multimode quantum memories, and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss-and-noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle nonidealities, that this scheme achieves a secret-key rate that surpasses the Takeoka-Guha-Wilde bound---a recently found fundamental limit to the rate-vs-loss scaling achievable by any QKD protocol over a direct optical link---thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement-distillation rate, as a function of the number of repeater nodes, total range, and various loss-and-noise parameters of the system. We extend our theoretical analysis to encompass sources with nonzero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.