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：量子网络的关键依赖于分布在远距离节点间的高质量量子比特纠缠对（即纠缠链路）的可用性。由于存在时间相关噪声（即退相干），维持这些链路的品质极具挑战性。纠缠纯化协议通过将多个低质量纠缠态转化为少量高质量纠缠态提供了解决方案。本研究提出一种分析框架，用于评估结合纠缠消耗、退相干与纠缠纯化的纠缠缓冲配置性能。我们引入两个关键指标：可用性（纠缠链路存在的稳态概率）与平均消耗保真度（消耗链路稳态品质的量化指标）。随后研究双节点系统，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。我们将该配置建模为连续时间随机过程，并推导出性能指标的解析表达式。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。针对采用经典双局域克利福德纯化协议的缓冲系统，我们进一步界定了这些性能指标。重要的是，分析表明在存在噪声的情况下，持续纯化缓冲纠缠可提升平均消耗保真度——即使部分缓冲纠缠因纯化失败而被丢弃。