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A quantum network distributes quantum entanglements between remote nodes, and is key to many applications in secure communication, quantum sensing and distributed quantum computing. This paper explores the fundamental trade-off between the throughput and the quality of entanglement distribution in a multi-hop quantum repeater network. Compared to existing work which aims to heuristically maximize the entanglement distribution rate (EDR) and/or entanglement fidelity, our goal is to characterize the maximum achievable worst-case fidelity, while satisfying a bound on the maximum achievable expected EDR between an arbitrary pair of quantum nodes. This characterization will provide fundamental bounds on the achievable performance region of a quantum network, which can assist with the design of quantum network topology, protocols and applications. However, the task is highly non-trivial and is NP-hard as we shall prove. Our main contribution is a fully polynomial-time approximation scheme to approximate the achievable worst-case fidelity subject to a strict expected EDR bound, combining an optimal fidelity-agnostic EDR-maximizing formulation and a worst-case isotropic noise model. The EDR and fidelity guarantees can be implemented by a post-selection-and-storage protocol with quantum memories. By developing a discrete-time quantum network simulator, we conduct simulations to show the characterized performance region (the approximate Pareto frontier) of a network, and demonstrate that the designed protocol can achieve the performance region while existing protocols exhibit a substantial gap., Comment: Currently under review at IEEE/ACM Transactions on Networking

Quantum entanglement distribution between remote nodes is key to many promising quantum applications. Existing mechanisms have mainly focused on improving throughput and fidelity via entanglement routing or single-node scheduling. This paper considers entanglement scheduling and distribution among many source-destination pairs with different requests over an entire quantum network topology. Two practical scenarios are considered. When requests do not have deadlines, we seek to minimize the average completion time of the communication requests. If deadlines are specified, we seek to maximize the number of requests whose deadlines are met. Inspired by optimal scheduling disciplines in conventional single-queue scenarios, we design a general optimization framework for entanglement scheduling and distribution called ESDI, and develop a probabilistic protocol to implement the optimized solutions in a general buffered quantum network. We develop a discrete-time quantum network simulator for evaluation. Results show the superior performance of ESDI compared to existing solutions.