Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs

We study the limits of entanglement distribution using a chain of quantum repeaters that have memory and perform entanglement swapping to connect short-distance into long-distance entanglement. We take time to be slotted: each node can perform heralded entanglement generation with its neighbor(s) and an entanglement swapping measurement per time slot. Moreover, qubits stored at the repeaters are subjected to a maximum storage time, known as cutoff – used to ensure a minimum fidelity of the resulting end-to-end states.

Operations are performed according to a global-knowledge policy that determines which node performs what operation in each time step, taking into account global knowledge of the state of the entanglement already produced.

Here, we find global-knowledge policies that minimize the expected time required to produce end-to-end entanglement in homogeneous repeater chains. We model the evolution of this system as a Markov decision process, and find optimal policies using dynamic programming. We show that the advantage in expected delivery time provided by a global-knowledge optimal policy compared to a policy in which nodes only use local information increases with increasing number of nodes and decreasing probability of successful entanglement swap. Our work sheds light on how to distribute entangled pairs in large quantum networks using a chain of intermediate repeaters with cutoffs.