Short answer: In a quantum network, entanglement between distant end points is built from short links that succeed only with some probability, so the rate normally falls as distance grows. Theory papers propose ways to soften or avoid that fall, using nodes that fuse several links at once, using multiplexing across several memories, and cutting off old links. These are protocol analyses and models, not network deployments.
The rate problem
A quantum network generates long-distance entanglement from heralded entanglement between physical neighbours, which succeeds with some probability and otherwise raises a failure flag, followed by entanglement swaps that join links. A 2023 arXiv paper (2307.01406) describes the basic operations in just this way, and adds the removal of any link older than a cutoff time, so that low-quality entanglement does not linger in the network, and the consumption of links in the background by applications. Because each step is probabilistic, rates over long chains of links depend strongly on how the nodes combine them.
Fusing many links
A 2022 npj Quantum Information paper develops a protocol where a repeater node uses n-qubit GHZ projective measurements to fuse n successfully entangled links, which are Bell pairs shared across n edges at that node. The authors say implementing n-fusion for n of 3 or more is in principle not much harder than 2-fusion, meaning Bell-basis measurement, in solid-state qubit memories. By connecting the problem to a modified version of site-bond percolation, they find that even with lossy link generation and probabilistic fusion, allowing 3-fusions at the nodes lets entanglement between two end parties be generated at a rate that stays constant as the distance between them grows. They also state a proof that this property cannot be reached by any protocol built only from Bell measurements and multiplexing.
Multi-qubit nodes and multiplexing
A 2017 Quantum Science and Technology paper looks at the other bottleneck: networks spanning more than a few kilometres are limited by the time for information to travel between nodes. It analyses protocols that get round this using multi-qubit nodes and multiplexing, and examines the network parameters that set each protocol's performance. The authors model achievable entangling rates using the anticipated near-term performance of nitrogen-vacancy centres and other candidate platforms, and say the analysis points to the parameters where improvements would matter most for prototype networks.
Cutoffs and consumption
The 2023 paper studies what happens when links are consumed by applications as fast as they are made. It reports that the expected virtual neighbourhood size drops rapidly towards zero when the consumption rate rises above the generation rate, and that in tree topologies with high generation rates the consumption rate affects performance more strongly than the minimum fidelity required.
What this does not show
These are theoretical and modelled results with assumed probabilities and memory behaviour. They say what rate scaling is possible in principle, not what a real network achieves today.
FAQ
Why does entanglement rate fall with distance?
Link generation and swapping are probabilistic, and the more links in a chain the less likely all of them succeed in time.
Can the rate stay constant with distance?
A 2022 paper shows this is possible with 3-fusion at the nodes, and proves it cannot be done with Bell measurements and multiplexing alone.
What does a cutoff time do?
It removes links older than a set age so low-quality entanglement does not remain in the network.
What is multiplexing used for?
Using several memories per node to get past the propagation-time bottleneck over long distances, according to the 2017 analysis.
Are these networks built?
These papers describe protocols and models, and do not describe deployed networks.
All field notes