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.

Entanglement distribution via probabilistic entanglement swapping across a quantum repeater chain connecting two quantum nodes is a challenging problem. The difficulty lies in the exponential number of possible swapping structures within the repeater chain, necessitating efficient search algorithms, especially as the chain length increases. In this paper, we first explore the algorithmic design to facilitate the search for the optimal swapping structure along a repeater chain, aiming to maximize the entanglement distribution rate. Second, we examine the computational complexities of various algorithms and find that prior approaches exhibit excessively high complexities. Thus, we propose an efficient dynamic programming-based algorithm, FastHED, that leverages heuristics to expedite the search for the optimal swapping structure. Our theoretical analysis reveals that the upper bound of the proposed algorithm’s computational complexity is$O(n(\log n)^{3})$(more precisely,$O(n(\log n)^{2} \log \log n)$when$n\le 2^{29}$), a significant improvement over the existing algorithm with a complexity of$O(n^{2} \log n)$, where n denotes the repeater chain’s length. Additionally, we design a best-first framework to evaluate the performance of different algorithms. Numerical results show that our algorithm achieves a higher average entanglement distribution rate than existing algorithms.