Quantum network applications impose a variety of requirements on entanglement resources in terms of rate, fidelity, latency, and more. The repeaters in the quantum network must combine good methods for entanglement generation, effective entanglement distillation, and smart routing protocols to satisfy these application requirements. In this work, we focus on entanglement distillation in a linear chain of quantum repeaters. While conventional approaches reuse the same distillation scheme over multiple hop lengths after entanglement swaps, we propose a novel adaptive quantum error correction (QEC) scheme that boosts end-to-end metrics. Specifically, depending on the network operating point, we adapt the code used in distillation over successive rounds to monotonically increase the rate while also improving fidelity. We demonstrate the effectiveness of this strategy using three codes, with parameters [[9,1,3]], [[9,2,3]], [[9,3,3]], and a new performance metric, efficiency, that incorporates both overall rate and fidelity. Since the minimum input fidelity for QEC-based distillation is high, we then extend our study to include non-QEC-based purification protocols, specifically DEJMPS since it outperforms others. We compare the performance of end-to-end DEJMPS against adapting from DEJMPS to QEC once DEJMPS improves the initial fidelity to the threshold for QEC. Through a refined efficiency metric, we illuminate the regime where QEC is beneficial. These results provide a detailed outlook for entanglement purification and distillation in first and second generation quantum repeaters.

翻译：量子网络应用对纠缠资源在速率、保真度、延迟等方面提出了多样化的要求。量子网络中的中继器必须结合良好的纠缠生成方法、有效的纠缠蒸馏方案以及智能的路由协议，以满足这些应用需求。在本工作中，我们聚焦于线性量子中继器链中的纠缠蒸馏问题。传统方法在纠缠交换后，对多个跳数长度重复使用相同的蒸馏方案，而我们提出了一种新颖的自适应量子纠错方案，该方案能提升端到端性能指标。具体而言，根据网络运行点，我们在连续轮次中自适应调整蒸馏所用的编码，以单调提升速率并同时改善保真度。我们使用参数分别为[[9,1,3]]、[[9,2,3]]、[[9,3,3]]的三种编码，以及一个结合了总速率和保真度的新性能指标——效率，来论证该策略的有效性。由于基于量子纠错的蒸馏所需的最小输入保真度较高，我们随后将研究扩展到包含非量子纠错基础的纯化协议，特别是性能优于其他方案的DEJMPS协议。我们比较了端到端DEJMPS方案与从DEJMPS自适应切换到量子纠错方案（一旦DEJMPS将初始保真度提升至量子纠错阈值）的性能。通过一个改进的效率指标，我们阐明了量子纠错方案具有优势的运行区间。这些结果为第一代和第二代量子中继器中的纠缠纯化与蒸馏提供了详细的前景展望。