We study entanglement generation in a quantum network where repeater nodes can perform n-qubit Greenberger-Horne-Zeilinger(GHZ) swaps, i.e., projective measurements, to fuse n imperfect-Fidelity entangled-state fragments. We show that the distance-independent entanglement distribution rate found previously for this protocol, assuming perfectly-entangled states at the link level, does not survive. This is true also in two modified protocols we study: one that incorporates l→1 link-level distillation and another that spatially constrains the repeater nodes involved in the swaps. We obtain analytical formulas for a GHZ swap of multiple Werner states, which might be of independent interest. Whether the distance-independent entanglement rate might re-emerge with a spatio-temporally-optimized scheduling of GHZ swaps and multi-site block-distillation codes remains open.
@article{arxiv.2306.03319,
title = {Entanglement distribution in two-dimensional square grid network},
author = {Eneet Kaur and Saikat Guha},
journal= {arXiv preprint arXiv:2306.03319},
year = {2023}
}