We consider problems of distributing high-fidelity entangled states across nodes of a quantum network. We consider a repeater-based network architecture with entanglement swapping (fusion) operations for generating long-distance entanglements, and purification operations that produce high-fidelity states from several lower-fidelity states. The contributions of this paper are two-fold: First, while there have been several works on fidelity-aware routing and incorporating purification into routing for generating EPs, this paper presents the first algorithms for optimal solutions to the high-fidelity EP distribution problem. We provide a dynamic programming algorithm for generating the optimal tree of operations to produce a high-fidelity EP, and an LP-based algorithm for generating an optimal collection of trees. Second, following the EP algorithms, this paper presents the first algorithms for the high-fidelity GHZ-state distribution problem and characterizes its optimality. We evaluate our techniques via simulations over NetSquid, a quantum network simulator.
@article{arxiv.2503.14712,
title = {Distribution and Purification of Entanglement States in Quantum Networks},
author = {Xiaojie Fan and Yukun Yang and Himanshu Gupta and C. R. Ramakrishnan},
journal= {arXiv preprint arXiv:2503.14712},
year = {2025}
}