Stochastic Analysis of Entanglement-assisted Quantum Communication Channels

TL;DR

This paper develops a stochastic queueing model for quantum communication networks involving entanglement-assisted channels, analyzing their asymptotic behavior using advanced probabilistic methods.

Contribution

It introduces a multi-scale queueing model for quantum networks and proves limit theorems using stochastic averaging and differential equations.

Findings

Proves a Functional Law of Large Numbers for the quantum queue system.

Establishes a Functional Central Limit Theorem for the averaged queue dynamics.

Provides a probabilistic framework for analyzing quantum communication network performance.

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.