Timely availability of high-fidelity entanglement is essential for emerging quantum networks. This paper introduces the Age of Entanglement (AoE) as a novel performance metric that captures the freshness of bipartite entanglement under continuous distribution in quantum repeater chains. AoE extends classical Age of Information (AoI)-based metrics to quantum networking by capturing storage, decoherence, and probabilistic entanglement generation and swapping. We study a satellite-assisted quantum repeater network in which entangled pairs are generated probabilistically, stored in quantum memories that suffer from decoherence, and combined to form end-to-end entangled links. Satellite-ground connectivity is intermittent and modeled as a two-state Markov chain. The resulting AoE minimization problem is formulated as an infinite-horizon Markov decision process (MDP), where control actions determine when to generate, store, or swap entangled pairs under stochastic link availability and memory degradation. Using relative value iteration, we characterize AoE-optimal policies and evaluate their performance numerically. Our results highlight the impact of decoherence, imperfect operations, and visibility dynamics, and show that the proposed dynamic policies significantly outperform swap-as-soon-as-possible and greedy entanglement generation strategies. Our results provide practical design and control guidelines for satellite-enabled quantum repeater chains supporting continuous entanglement distribution.

翻译：高保真纠缠态的及时可用性对新兴量子网络至关重要。本文提出纠缠时效（AoE）作为一种新颖的性能度量指标，用于刻画量子中继链中连续分发下的双体纠缠态新鲜度。AoE通过捕捉存储、退相干以及概率性纠缠生成与交换过程，将经典的基于信息时效（AoI）的度量体系扩展至量子网络领域。我们研究一种卫星辅助量子中继网络，其中纠缠对以概率方式生成，存储在受退相干影响的量子存储器中，并通过组合形成端到端纠缠链路。星地连接具有间歇性，采用两态马尔可夫链建模。由此构建的AoE最小化问题被表述为无限时域马尔可夫决策过程（MDP），其控制动作决定了在随机链路可用性与存储器性能退化的约束下，何时生成、存储或交换纠缠对。通过相对值迭代算法，我们刻画了AoE最优策略并进行了数值性能评估。研究结果揭示了退相干、非完美操作及可见度动态的影响，表明所提出的动态策略显著优于"尽快交换"与贪婪纠缠生成策略。本研究为支持连续纠缠分发的卫星量子中继链提供了实用的设计与控制指导原则。