Dynamic Queuing Analysis and Buffer Management for Entanglement Swapping Buffers with Noise

Entanglement swapping is a core operation in a quantum network. It consumes a pair of entanglements to build a remote entanglement between two parties without direct interaction. In a buffered quantum network, unpaired entanglements can be stored in a quantum buffer for future uses. However, suffering from noises in the quantum buffer, fidelities of buffered entanglements degrade exponentially over time. Entanglements with low fidelity are no longer suitable for certain quantum applications and ought to be discarded. This paper analyzes the dynamic queuing process for a pair of link-level quantum buffers in entanglement swapping. By modeling the quantum buffer pair as a double-sided queue, we derive a closed-form buffering time distribution for every incoming entanglement with respect to the real-time buffer backlog. The distribution reveals the probability that entanglement will be discarded due to low fidelity and helps us design an active buffer management policy that controls the buffer backlog with negligible impact on the entanglement swapping throughput. A discrete-time simulator is developed to demonstrate the correctness of our analysis result and validate the effectiveness of our proposed policy.