A Queuing-Theoretic Model for Quantum Repeater Chains with Sequential Swapping

Quantum repeater chains are fundamental quantum network building blocks, enabling entanglement generation between distant nodes through link-level entanglement generation and entanglement swapping. The end-to-end (E2E) entanglement generation rate and fidelity of repeater chains are key performance measures that impose fundamental constraints on what can be achieved by quantum networks. Previous work has mainly characterized these measures in the one-shot regime, where the chain generates a single E2E entangled state at a time, under various operational assumptions. This work presents a continuous-time queueing-theoretic model yielding analytical expressions for the E2E entanglement generation rate, fidelity, and entanglement-based BB84 secret-key rate of quantum repeater chains performing sequential entanglement swapping. The analysis focuses on chains that continuously generate a stream of E2E entangled states, which is more practical than the one-shot regime. It takes into account noisy link-level entanglement with different generation models, such as source-in-the-middle and meet-in-the-middle schemes, classical communication delay, and memory decoherence and gate-noise in the form of dephasing and depolarizing errors. The analytical expressions presented are applied to numerically study the number of repeaters that maximize fidelity or SKR based on the chain's E2E distance, and the impact of improving gate-noise and memory coherence times to E2E performance.