Multi-Pair Fidelity-Aware Rate Allocation in a Quantum Network: Approximation Schemes

2026-08-11

AI Summary

This work addresses the rate allocation problem for multiple user pairs in quantum networks under practical constraints, including limited link capacities, probabilistic entanglement swapping, and heterogeneous end-to-end fidelities. The study investigates three optimization objectives: maximizing total throughput, maximizing total throughput subject to minimum rate guarantees, and achieving max-min fairness. It establishes, for the first time, that all three fidelity-aware rate allocation problems are NP-hard. To tackle these challenges, the authors propose a unified fully polynomial-time approximation scheme (FPTAS) based on dynamic programming that jointly optimizes transmission rates and end-to-end fidelity. Extensive experiments on random quantum network topologies demonstrate the efficiency and practicality of the proposed algorithm.

Abstract

Entanglement distribution in quantum networks must jointly account for limited link capacities, probabilistic entanglement swapping, and heterogeneous link fidelities. In this paper, we study multi-pair fidelity-aware rate allocation in quantum networks. We formulate three rate-allocation problems: rate sum, rate sum subject to minimum-rate constraints, and max-min fairness. Prior work has studied a special case of the rate sum problem, where all links have identical fidelity. This special case admits a polynomial-time algorithm. We prove that all three problems are NP-hard. We then study optimization versions of these problems which maximize the minimum end-to-end fidelity subject to throughput or fairness requirements. We present fully polynomial-time approximation schemes (FPTAS) for solving these optimization problems. Experiments on randomly generated networks demonstrate the computational effectiveness of the proposed schemes.

Problem

• quantum network
• entanglement distribution
• fidelity-aware rate allocation
• NP-hard
• multi-pair

Innovation

• quantum networks
• fidelity-aware rate allocation
• NP-hardness
• FPTAS
• entanglement distribution