Stochastic Analysis of Entanglement-assisted Quantum Communication Channels

• URL: http://arxiv.org/abs/2412.16157v1
• Date: Fri, 20 Dec 2024 18:59:58 GMT
• Title: Stochastic Analysis of Entanglement-assisted Quantum Communication Channels
• Authors: Karim S. Elsayed, Olga Izyumtseva, Wasiur R. KhudaBukhsh, Amr Rizk,
• Abstract summary: We present a queueing model for quantum communication networks, inspired by its technological promise and recent experimental successes. The model consists of a primary queue and a service queue where Bell pairs are formed and stored. We study the behaviour of this multi-scale queueing system utilizing the theory of averaging principle.
• Score: 2.1786693199184346
• License:
• Abstract: In this paper, we present a queueing model for quantum communication networks, a rapidly growing field of research inspired by its technological promise and recent experimental successes. The model consists of a primary queue and a service queue where Bell pairs are formed and stored. The Bell pairs are by nature 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 utilizing the theory of 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. Our proofs are probablistic and rely on the stochastic analysis of Stochastic Differential Equations (SDEs) driven by Poisson Random Measures.

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