Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs

TL;DR

This paper investigates optimal strategies for distributing entanglement across quantum repeater chains with memory cutoffs, using Markov decision processes to minimize expected delivery time in large quantum networks.

Contribution

It introduces global-knowledge policies for entanglement distribution that outperform local policies, especially as network size increases and success probabilities decrease.

Findings

Optimal policies significantly reduce expected entanglement delivery time.

Global-knowledge policies outperform local policies in larger networks.

Advantage of global policies grows with network size and lower success probability.

Abstract

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.