Analysis of Asynchronous Protocols for Entanglement Distribution in Quantum Networks

TL;DR

Addressing the practical challenge of entanglement distribution in large quantum networks under asynchronous operation, memory decoherence, nonuniform repeater spacings, and classical communication delays. The authors analyze two minimal asynchronous protocols, sequential and parallel, with a shared noise model and a memory-cutoff strategy, and evaluate end-to-end metrics $R_{e2e}$, $F_{e2e}$, and $S$ on SURFnet. They derive expressions for end-to-end fidelity and rate, compare performance via Monte Carlo and discrete-event simulations, and show the sequential protocol is competitive with the parallel protocol while offering simpler implementation; cutoff strategies improve fidelity at the cost of rate, and classical delays substantially reduce realistically achievable SKR. The work provides guidance for quantum network design, suggesting hop-by-hop sequential schemes as robust, scalable primitives and highlighting future directions such as purification and routing under realistic constraints.

Abstract

The distribution of entanglement in quantum networks is typically approached under idealized assumptions such as perfect synchronization and centralized control, while classical communication is often neglected. However, these assumptions prove impractical in large-scale networks. In this paper, we present a pragmatic perspective by exploring two minimal asynchronous protocols: a parallel scheme generating entanglement independently at the link level, and a sequential scheme extending entanglement iteratively from one party to the other. Our analysis incorporates non-uniform repeater spacings and classical communications and accounts for quantum memory decoherence. We evaluate network performance using metrics such as entanglement bit rate, end-to-end fidelity, and secret key rate for entanglement-based quantum key distribution. Our findings suggest the sequential scheme's superiority due to comparable performance with the parallel scheme, coupled with simpler implementation. Additionally, we impose a cutoff strategy to improve performance by discarding attempts with prolonged memory idle time, effectively eliminating low-quality entanglement links. Finally, we apply our methods to the real-world topology of SURFnet and report the performance as a function of memory coherence time.

Figures (7)

• Figure 1: Two asynchronous protocols for entanglement distribution studied in this paper.
• Figure 2: A repeater chain with one repeater. Solid lines show the ebit rate and dashed lines show the SKR of the associated protocols. For each color, the solid line indicates the ebit rate and the dashed line represents the SKR.
• Figure 3: The upper panels show sample plots of the SKR as a function of cutoff using $7$ repeaters on three different distances (points in the lower panels (color coded)) for $L_{e2e}=200,300$ and $400$ km (blue, orange, green), respectively. The dashed lines in the top plot indicate the SKR without cutoff for the corresponding distance indicated in the bottom plots. The lower panels show maximal SKR for a given distance and coherence time by optimizing the cutoff. We show two contour lines at $10^0$ and $10^2$ SKRs as a guide to eyes. The infeasible regions correspond to the case error rates are so large that the secret fraction (\ref{['eq:secret-fraction']}) vanishes.
• Figure 4: Feasible regimes of parameters for different values (color coded) of noise parameters $F$ defined in (\ref{['eq:link-level-epr']}) and $\mu$ in (\ref{['eq:2q-depolarizing']}) and insertion loss $p_\text{link}$ in (\ref{['eq:link-level-prob']}). The solid (dashed) lines are the boundaries of the feasible region for the case with (without) cutoff. Each legend indicates the values for $(F, \mu, p_\text{link})$.
• Figure 5: SKR (a) and fidelity (b) with and without classical comm delay. The solid and dashed lines of the same color represent the same protocol with and without classical comm delay, respectively.