Policies for elementary link generation in quantum networks

Protocols in a quantum network involve multiple parties performing actions on their quantum systems in a carefully orchestrated manner over time in order to accomplish a given task. This sequence of actions over time is often referred to as a strategy, or policy. In this work, we consider policy optimization in a quantum network. Specifically, as a first step towards developing full-fledged quantum network protocols, we consider policies for generating elementary links in a quantum network. We start by casting elementary link generation as a quantum partially observable Markov decision process, as defined in [Phys. Rev. A 90, 032311 (2014)]. Then, we analyze in detail the commonly used memory cutoff policy. Under this policy, once a link is established it is kept in quantum memory for some amount $t^{\star}$ of time, called the cutoff, before it is discarded and link generation is reattempted. For this policy, we determine the average quantum state of the elementary link as a function of time for an arbitrary number of nodes in the link, as well as the average fidelity of the link as a function of time for any noise model for the quantum memories. We then show how optimal policies can be obtained in the finite-horizon setting using dynamic programming.