Rethinking Quantum Repeaters: Balancing Scalability, Feasibility, and Interoperability

TL;DR

The paper tackles the challenge of long-distance quantum communication by proposing SEG-ED, a connectionless quantum repeater architecture that uses sequential entanglement generation with error detection instead of full quantum error correction. By encoding memories with simple codes and aborting rounds upon error detection, SEG-ED aims to balance scalability, feasibility, and interoperability with existing telecom infrastructure, and it is benchmarked via a QKD setup along repeater chains. The authors develop a detailed performance framework, including memory/decoherence models, link-level and logical entanglement procedures, and a pipeline-based SKR analysis, comparing SEG-ED to SEG-noED, SEG-prob, and PEG-ED across hardware stages. The results indicate potential continental-scale reach (stage-2) and even global reach (stage-3) while highlighting resource efficiency gains and practical deployment prospects in real-world networks.

Abstract

Quantum repeaters are enabling technologies for long-distance quantum communications. Despite the significant progress in the field, we still not only face implementation challenges but also need theoretical solutions that better meet all the desired design criteria. Preliminary solutions for quantum repeaters often do not scale well, while the most advanced solutions are so demanding that their implementation may take a long time and require substantial changes to current telecom infrastructure. In this paper, we propose a compromise solution that is not only scalable in the mid-to-long term but also adapts well to the realities of the backbone networks in the current Internet infrastructure. The key ideas behind our solution are twofold. First, we use a connectionless approach to entanglement swapping, allowing our solution to benefit from the same features as packet-switched networks. Second, we employ simple error detection, rather than more complicated error correction, techniques to make our solution sufficiently scalable in the face of errors. This is achieved without requiring overly demanding specifications for the physical devices needed in the network. We test this idea in a quantum key distribution (QKD) setting over a repeater chain and demonstrate how trust-free continental QKD can be achieved through several stages of development.

Figures (11)

• Figure 1: A schematic of a quantum repeater network, with a certain path of seven repeater nodes connecting two users. Solid lines represent quantum and classical channels and circles represent nodes.
• Figure 2: Repeater chain setup with each node containing two types of quantum memories. Squares (circles) represent data (communication) qubits. Single solid lines represent quantum channels. Double solid lines represent classical channels.
• Figure 3: Distribution of a raw key bit using SEG-ED, where, for demonstration purposes, we have assumed that ${N_{\text{mux}}} = n_{\text{code}} = 3$. (a) First hop in the distribution round: Alice and $\mathsf{R}_{1}$ share an encoded entangled state. After encoding, Alice immediately uses the QKD-specific decoder in Jing_Simple:2021 to obtain her raw key bit, $b_{\text{A}}$, projecting the data qubits in $\mathsf{R}_{1}$ onto a state correlated to it. Alice transmits the results of the encoding to $\mathsf{R}_{1}$. (b) The $(i+1)$-th hop, involving the $i$-th logical swap: Nodes $\mathsf{R}_{i}$ and $\mathsf{R}_{i+1}$ prepare logical entanglement. Immediately after encoding, $\mathsf{R}_{i}$ performs the logical swapping to teleport the data qubit correlated with $b_{\text{A}}$ to $\mathsf{R}_{i+1}$, and transmits the results of the local operations. After receiving them, $\mathsf{R}_{i+1}$ determines if an error is detected and, if so, aborts the distribution (bit $b_{\text{A}}$ is discarded during the QKD sifting stage). Otherwise, distribution continues. (c) Last hop, reaching Bob: Node $\mathsf{R}_{N_r}$ acts as in \ref{['fig:protocol_desc']}(b). After encoding, Bob immediately uses the QKD-specific decoder to obtain his raw key bit, $b_{\text{B}}$. Once Bob receives the results of the final LSWP, he discards the raw key bit if an error is detected. Otherwise, he adjusts its value classically according to the Pauli frame. In all parts: squares (circles) represent data (communication) qubits; diamonds represent classical information; dashed lines represent entanglement generation attempts through photonic transmissions; twisted lines represent entanglement; double solid lines represent classical communications channels, and arrows below them indicate the direction of the communication. Only active resources are depicted at each step.
• Figure 4: Performance metrics versus hop length, $L_0$. (a) Maximum range, $L_\text{max}$, for which $r_{\infty} > 0$. (b) Secret key rate, $K$, at $L = 1000km$ and $L = 1500km$. In all graphs: solid lines represent our proposal, SEG-ED; dashed lines represent SEG-noED, the unencoded SEG protocol where the swapping operation is implemented using deterministic BSMs; dash-dotted lines represent the unencoded SEG-prob protocol that relies on probabilistic but noiseless BSMs; and dotted lines correspond to PEG-ED with 3QRC for error detection. Thick dashed lines in (b) represent the PLOB bound Pirandola_PLOB:2017 when considering a fiber attenuation constant of $\alpha_\text{ch} = 0.1dB\per km$, corresponding to stage 3, and a clock rate of 1 GHz.
• Figure 5: Secret key rate, $K$, against total distance between the users, $L$, for a hop length of $L_0=50km$. The PLOB bound Pirandola_PLOB:2017 when considering a fiber attenuation constant of $\alpha_\text{ch} = 0.1dB\per km$ (i.e., corresponding to the value in stage 3) and a clock rate of 1 GHz is drawn with a thick, dashed, black line.