Distribution and Purification of Entanglement States in Quantum Networks

2025-03-18

AI Summary

Low efficiency and uncontrollable fidelity in end-to-end distribution of high-fidelity entangled pairs (EPs) and Greenberger–Horne–Zeilinger (GHZ) states hinder scalable quantum networking. Method: We propose a relay-oriented joint optimization framework: (i) the first dynamic programming–based optimal operation tree for single-pair EP distribution; (ii) an LP model for coordinated multi-EP distribution; and (iii) rigorous characterization of optimality conditions for GHZ-state distribution. The method integrates entanglement swapping, distillation-based purification, and resource scheduling. Contribution/Results: Evaluated on NetSquid, our approach significantly improves fidelity and success probability over heuristic baselines while reducing resource overhead by 37%. It constitutes the first systematic solution for large-scale quantum networks that simultaneously achieves theoretical optimality and engineering feasibility—enabling scalable, fidelity-controllable quantum network protocols.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Distribute high-fidelity entangled states in quantum networks.
• Develop algorithms for optimal entanglement purification and routing.
• Solve high-fidelity GHZ-state distribution and evaluate via simulations.

Innovation

• Dynamic programming for optimal entanglement purification trees
• LP-based algorithm for optimal tree collections
• First algorithms for high-fidelity GHZ-state distribution