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Policies for elementary link generation in quantum networks

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Document pages: 64 pages

Abstract: Protocols in a quantum network involve multiple parties performing actions ontheir quantum systems in a carefully orchestrated manner over time in order toaccomplish a given task. This sequence of actions over time is often referredto as a strategy, or policy. In this work, we consider policy optimization in aquantum network. Specifically, as a first step towards developing full-fledgedquantum network protocols, we consider policies for generating elementary linksin a quantum network. We start by casting elementary link generation as aquantum partially observable Markov decision process, as defined in [Phys. Rev.A 90, 032311 (2014)]. Then, we analyze in detail the commonly used memorycutoff policy. Under this policy, once an elementary link is established it iskept in quantum memory for some amount $t^{ star}$ of time, called the cutoff,before it is discarded and the elementary link generation is reattempted. Forthis policy, we determine the average quantum state of the elementary link as afunction of time for an arbitrary number of nodes in the link, as well as theaverage fidelity of the link as a function of time for any noise model for thequantum memories. Finally, we show how optimal policies can be obtained in thefinite-horizon setting using dynamic programming. By casting elementary linkgeneration as a quantum decision process, this work goes beyond the analyticalresults derived here by providing the theoretical framework for performingreinforcement learning of practical quantum network protocols.

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