Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs

Quantum repeater chains can be used to distribute bipartite entanglement among two end nodes. We study the limits of entanglement distribution using a chain of quantum repeaters that have quantum memories. A maximum storage time, known as cutoff, is enforced on these memories to ensure high-quality end-to-end entanglement. To generate end-to-end entanglement, the nodes can perform the following operations: wait, attempt the generation of an elementary entangled link with its neighbor(s), or perform an entanglement swapping measurement. Nodes follow a policy that determines what operation they must perform in each time step. Global-knowledge policies take into account all the information about the entanglement already produced. Here, we find global-knowledge policies that minimize the expected time to produce end-to-end entanglement. We model the evolution of this system as a Markov decision process, and find optimal policies using value and policy iteration. We compare optimal global-knowledge policies to a policy in which nodes only use local information. The advantage in expected delivery time provided by an optimal global-knowledge policy increases with increasing number of nodes and decreasing probability of successful entanglement swap. The advantage displays a non-trivial behavior with respect to the cutoff time and the probability of successful entanglement generation at the elementary link level. Our work sheds light on how to distribute entangled pairs in large quantum networks using a chain of intermediate repeaters with cutoffs.