Markov Chain Model of Entanglement Setup in Noisy Dynamic LEO Satellite Networks

TL;DR

This work addresses entanglement distribution in dynamic LEO satellite networks by formulating a Markov-chain model with a two-dimensional state space over memory storage age $i_{store}$ and inter-satellite distance $d$. It derives closed-form expressions for four core metrics—request satisfaction rate, average waiting time, link utilization, and average fidelity of consumed links—while explicitly accounting for beam diffraction, pointing errors, polarization rotation, and decoherence in both the free-space channel and quantum memories. The results reveal trade-offs: higher request rates yield faster link consumption with higher fidelity but potentially lower satisfaction due to limited generation speed, while lower rates enable longer storage at the cost of decoherence-driven fidelity loss; polarization rotation can be neglected for short hops, simplifying design. Practically, the model yields guidance on maximum one-hop distances ($ oughly 40$–$50$ km), cutoff times ($T_{cutoff}\lesssim 0.3$ s), and aperture requirements to meet $F_{th}=0.5$, enabling optimized entanglement routing for scalable global quantum communication.

Abstract

Quantum entanglement routing in dynamic Low Earth Orbit (LEO) satellite networks is important for achieving scalable and high-fidelity quantum communication. However, the dynamic characteristics of satellite network topology, limited quantum resources, and strict coherence time constraints pose significant challenges to reliable entanglement routing. An entanglement distribution analysis model for this unique environment is critical and helpful for entanglement routing research. We address the fundamental challenge of establishing and maintaining quantum entanglement links between satellites operating in free space, where links are subject to both transmission losses and quantum memory decoherence. This paper presents a comprehensive Markov chain model with a state space defined by link storage age and physical distance for analyzing entanglement distribution in noisy dynamic LEO satellite quantum networks. We construct transition matrices that capture system dynamics under varying request arrival rates, and derive analytical expressions for key performance metrics, including request satisfaction rate, average waiting time, link utilization efficiency, and average consumed link fidelity. Our analysis reveals that the critical trade-offs of higher request rates lead to faster link consumption with higher fidelity but potentially lower satisfaction rates, while lower request rates allow longer storage times at the cost of lower fidelity of increased decoherence effect. Moreover, this paper proves it is reasonable to leave out polarization rotation when the transmission distance is very short (40-50 km). In summary, this work provides theoretical foundations for designing and optimizing quantum entanglement distribution strategies in satellite networks, with applications to global-scale quantum communications.

Figures (9)

• Figure 1: 2-node
• Figure 2: EPR Pair Fidelity Timeline
• Figure 4: Single Photon Path
• Figure 5: Capture Probability ($q$)
• Figure 6: Initial Fidelity ($F_0'$)