Entanglement Distribution Over Quantum Networks with Fairness Guarantees

The entanglement distribution problem over quantum networks has been widely studied, with the objective of maximizing network throughput, that is, the number of entanglements distributed for all user pairs. However, most of the existing works only focus on throughput maximization while neglecting fairness considerations. In this paper, we first characterize the fairness of an entanglement distribution scheme by introducing a fairness factor based on Element-Wise Inequalities, referred to as EWI-fairness. The EWI-fairness requires that the entanglement distribution rate of each user pair exceeds a certain threshold, ensuring the fair distribution. Second, we enforce fairness guarantees into two existing distribution methods, Temporal Multiplexing Distribution (TMD) and Flow Multiplexing Distribution (FMD). Our theoretical analysis reveals that FMD-based scheme outperforms TMD-based scheme. Therefore, we focus on optimizing FMD-based scheme. Third, we formulate the fair entanglement distribution problem as a linear programming problem, where fairness requirements serve as constraints, aiming to identify the optimal FMD-based scheme with the highest throughput. Simulation results demonstrate that the optimized FMD-based scheme achieves a higher throughput compared to existing schemes under identical fairness requirements.