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