Advantages of Global Entanglement-Distillation Policies in Quantum Repeater Chains

TL;DR

This work addresses the challenge of optimizing distillation timing in quantum repeater chains to maximize the secret-key rate (SKR) under two-way classical communication. It compares global deterministic distillation policies (GD) against local deterministic policies (LD) by searching for near-optimal global schedules via Monte Carlo optimization within an MTP framework, across a broad parameter space. The results show that GD policies consistently outperform LD policies, with large-N regimes ($N>512$) achieving SKR improvements up to about two orders of magnitude and in some cases enabling secret communication that LD policies cannot. The findings imply that globally coordinated distillation decisions can substantially enhance end-to-end quantum communication, though the study is limited to DEJMPS EPPs and non-adaptive policies, suggesting avenues for future work with code-based EPPs and adaptive strategies.

Abstract

Quantum repeaters are essential for achieving long-distance quantum communication due to photon loss, which grows exponentially with the channel distance. Current quantum repeater generations use entanglement distillation protocols, where the decision of when to perform distillation depends on either local or global knowledge. Recent approaches for quantum repeaters, such as Mantri et al. (arXiv:2409.06152), consider using deterministic local decision policies for entanglement distillation. We ask whether global deterministic policies outperform local ones in terms of communication rate. We simulate equidistant repeater chains, assisted by two-way classical communication, and compare local and global policies for distillation decisions, spanning large distances and varying network and hardware parameters. Our findings show that global deterministic policies consistently outperform these local ones, and in some cases, determine whether secret communication is possible. For large repeater chains ($N>512$), global policies improve SKR by two orders of magnitude. These results suggest that local distillation decisions in quantum repeater chains may not be optimal, and may inform future protocol design.

Figures (4)

• Figure 1: Secret Key Rate (SKR) vs. Distance for $\eta = 1$ and $\epsilon = 0.001$, comparing mantri_comparing_2024 (solid colored curves for different $N$ values) against the bounds from guha_rate-loss_2015. Dotted color-coded curves are the three-piece upper bounds $R_N^{\rm UB}(L)$ for each $N$, where $R^{(UB)}(L)$ is their envelope. $R(L)$ and $R^{(0)}(L)$ are rate-loss envelopes as well. For complete definitions see guha_rate-loss_2015.
• Figure 2: Comparisons between GD policy and LD policy (SKR rule) for $N,M=512, \eta_c=0.3$. 3D plots show the number of distillation steps at each level of the protocol for varying distances. The plots are color coded by the output SKR. (a) shows the low error regime ($\epsilon_G = 10^{-4}$) where the GD policy distills once at level 5, and the SKR policy does not distill at all. (b) shows the moderate error regime ($\epsilon_G = 10^{-3}$), where the GD policy distills earlier at first, but then does not redundantly distill later on.
• Figure 3: Comparisons between GD policy and LD policy (SKR rule) for $N=4096,M=512, \epsilon_G=0.0001$. (a) shows the low coupling regime ($\eta_c=0.3$), and (b) shows the perfect coupling regime ($\eta_c=1.0$).
• Figure 4: Inverse plateau ratio (LD/GD) vs. number of segments ($N$) for different gate error rates ($\epsilon_G$) and coupling efficiencies ($\eta_c$). Each line represents a different multiplexing value ($M$) or distillation rule. For clarity, we plot the inverse of the plateau ratio $\mathrm{LD}/\mathrm{GD}=\text{plateau ratio}^{-1}$ such that values below 1 indicate an advantage for the GD policy. Data points have been omitted in either of these cases: (1) baseline LD policy produces a negligible SKR, yielding an undefined ratio, and (2) both baseline and GD policies produce negligible SKR values.