On the Capacity Region of a Quantum Network with Multiple Users and Applications

We investigate the capacity region of quantum networks that distribute entanglement concurrently among multiple applications, aiming to characterize their fundamental performance limits. Unlike existing works that address path selection, resource allocation, and data-plane protocols as separate problems, we present a unified formulation that jointly captures their interplay. Our model takes as input the network topology, active users, and optional fairness policies, and outputs for each user the set of paths, achievable entanglement rate, and fidelity.

The formulation is also application-aware: users can define reward functions quantifying the utility of entangled states at different fidelities. This leads to a non-convex multi-commodity flow problem, which we tackle with a nested iterative algorithm. The inner loop optimizes resource allocation over fixed paths, while the outer loop refines the path pool until convergence to a local (or global) optimum. The resulting solution naturally determines the network’s data plane, as it calculates the configuration and the schedule for every physical link in the network. Preliminary evaluations on grid, dumbbell, and random topologies show that our approach generalizes and outperforms existing baselines.