  We study the limits of bipartite entanglement distribution using a chain of
quantum repeaters that have quantum memories. To generate end-to-end
entanglement, each node can attempt the generation of an entangled link with a
neighbor, or perform an entanglement swapping measurement. A maximum storage
time, known as cutoff, is enforced on the memories to ensure high-quality
entanglement. Nodes follow a policy that determines when to perform each
operation. 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.
Our methods are based on Markov decision processes and value and policy
iteration. We compare optimal policies to a policy in which nodes only use
local information. We find that the advantage in expected delivery time
provided by an optimal global-knowledge policy increases with increasing number
of nodes and decreasing probability of successful swapping. Our work sheds
light on how to distribute entangled pairs in large quantum networks using a
chain of intermediate repeaters with cutoffs.
