Entanglement distribution is a key functionality of the Quantum Internet. However, quantum entanglement is very fragile, easily degraded by decoherence, which strictly constraints the time horizon within the distribution has to be completed. This, coupled with the quantum noise irremediably impinging on the channels utilized for entanglement distribution, may imply the need to attempt the distribution process multiple times before the targeted network nodes successfully share the desired entangled state. And there is no guarantee that this is accomplished within the time horizon dictated by the coherence times. As a consequence, in noisy scenarios requiring multiple distribution attempts, it may be convenient to stop the distribution process early. In this paper, we take steps in the direction of knowing when to stop the entanglement distribution by developing a theoretical framework, able to capture the quantum noise effects. Specifically, we first prove that the entanglement distribution process can be modeled as a Markov decision process. Then, we prove that the optimal decision policy exhibits attractive features, which we exploit to reduce the computational complexity. The developed framework provides quantum network designers with flexible tools to optimally engineer the design parameters of the entanglement distribution process.

翻译：纠缠分发是量子互联网的关键功能。然而，量子纠缠极其脆弱，易受退相干影响而退化，这严格约束了分发必须完成的时间范围。这一特性，加之用于纠缠分发的信道不可避免地受到量子噪声的影响，使得目标网络节点成功共享所需纠缠态之前，可能需要多次尝试分发过程。但并不能保证在相干时间所规定的时间范围内达成目标。因此，在需要多次分发尝试的噪声场景中，提前中止分发过程或许是明智之举。本文通过构建能够刻画量子噪声效应的理论框架，向"知止"的目标迈出了步伐。具体而言，我们首先证明纠缠分发过程可建模为马尔可夫决策过程。进而证明最优决策策略具有优越特性，并利用这些特性降低计算复杂度。所构建的框架为量子网络设计者提供了灵活的工具，使其能够以最优方式设计纠缠分发过程的各项参数。