  Distributing entanglement over long distances is one of the central tasks in
quantum networks. An important problem, especially for near-term quantum
networks, is to develop optimal entanglement distribution protocols that take
into account the limitations of current and near-term hardware, such as quantum
memories with limited coherence time. We address this problem by initiating the
study of quantum network protocols for entanglement distribution using the
theory of decision processes, such that optimal protocols (referred to as
policies in the context of decision processes) can be found using dynamic
programming or reinforcement learning algorithms. As a first step, in this work
we focus exclusively on the elementary link level. We start by defining a
quantum decision process for elementary links, along with figures of merit for
evaluating policies. We then provide two algorithms for determining policies,
one of which we prove to be optimal (with respect to fidelity and success
probability) among all policies. Then we show that the previously-studied
memory-cutoff protocol can be phrased as a policy within our decision process
framework, allowing us to obtain several new fundamental results about it. The
conceptual developments and results of this work pave the way for the
systematic study of the fundamental limitations of near-term quantum networks,
and the requirements for physically realizing them.
