Analysis on a Performance and Fairness Tradeoff in Entanglement Routing for Quantum Networks

Quantum networks offer the capability of transferring quantum information among remote nodes leveraging the phenomenon of quantum entanglement. A key challenge is entanglement routing, which routes quantum entanglement efficiently in a quantum network to satisfy specific objectives. We focus on an interesting hypothesis that arises from the probabilistic nature of quantum entanglement: There is a tradeoff between accommodating a higher number of quantum entanglements (performance) and serving a broader range of node pairs (fairness). To confirm this hypothesis, we formulate entanglement routing as a multi-objective optimization problem. Our numerical analysis reveals that the solutions of the model form a Pareto frontier, thereby validating the hypothesis. Furthermore, we compare the performance of existing algorithms against this Pareto frontier to understand how the algorithms balance performance and fairness. Our findings contribute to designing entanglement routing algorithms.