Stochastic Analysis of Entanglement-assisted Quantum Communication Channels
This work provides a theoretical framework for analyzing the asymptotic behavior of entanglement-assisted quantum communication channels, which is important for designing and optimizing future quantum networks.
This paper models a quantum communication network as a multi-scale queueing system with a fast service queue for Bell pair formation and storage. It proves a Functional Law of Large Numbers and a Functional Central Limit Theorem for the standard queue by averaging the fast service queue's dynamics.
We present a queueing model for a quantum communication network consisting of a primary queue and a service queue in which Bell pairs are formed and stored. The Bell pairs are inherently extremely short-lived rendering the service queue (the quantum queue) much faster than the primary queue. We study the asymptotic behaviour of this multi-scale queueing system via a stochastic averaging principle. We prove a Functional Law of Large Numbers (FLLN) and a Functional Central Limit Theorem (FCLT) for the standard queue averaging the dynamics of the fast service queue.