Quantum networks crucially rely on the availability of high-quality entangled pairs of qubits, known as entangled links, distributed across distant nodes. Maintaining the quality of these links is a challenging task due to the presence of time-dependent noise, also known as decoherence. Entanglement purification protocols offer a solution by converting multiple low-quality entangled states into a smaller number of higher-quality ones. In this work, we introduce a framework to analyse the performance of entanglement buffering setups that combine entanglement consumption, decoherence, and entanglement purification. We propose two key metrics: the availability, which is the steady-state probability that an entangled link is present, and the average consumed fidelity, which quantifies the steady-state quality of consumed links. We then investigate a two-node system, where each node possesses two quantum memories: one for long-term entanglement storage, and another for entanglement generation. We model this setup as a continuous-time stochastic process and derive analytical expressions for the performance metrics. Our findings unveil a trade-off between the availability and the average consumed fidelity. We also bound these performance metrics for a buffering system that employs the well-known bilocal Clifford purification protocols. Importantly, our analysis demonstrates that, in the presence of noise, consistently purifying the buffered entanglement increases the average consumed fidelity, even when some buffered entanglement is discarded due to purification failures.

翻译：量子网络的关键在于跨远距离节点分发高质量的双量子比特纠缠对，即纠缠链路。由于时变噪声（也称为退相干）的存在，维持这些链路的质量是一项具有挑战性的任务。纠缠纯化协议通过将多个低质量纠缠态转换为数量较少但质量更高的纠缠态，为此提供了解决方案。在本工作中，我们提出了一个分析框架，用于评估结合了纠缠消耗、退相干和纠缠纯化的纠缠缓冲设置的性能。我们提出了两个关键指标：可用性（即纠缠链路存在的稳态概率）和平均消耗保真度（用于量化所消耗链路的稳态质量）。随后，我们研究了一个双节点系统，其中每个节点拥有两个量子存储器：一个用于长期纠缠存储，另一个用于纠缠生成。我们将此设置建模为一个连续时间随机过程，并推导了性能指标的解析表达式。我们的研究结果揭示了可用性与平均消耗保真度之间的权衡关系。我们还对采用著名的双局域 Clifford 纯化协议的缓冲系统的这些性能指标给出了界限。重要的是，我们的分析表明，在存在噪声的情况下，持续纯化缓冲的纠缠能够提高平均消耗保真度，即使部分缓冲纠缠会因纯化失败而被丢弃。