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arXiv:2512.20047

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

Yifan Gao, Alvin Valera, Winston K. G. Seah

quant-phSubmitted Dec 23, 2025• Announced Dec 24, 2025• 0 citations• Revised Oct 6, 2026 (v4)
v1 · Dec 23, 2025v2 · Feb 27, 2026v3 · Mar 13, 2026v4 · Oct 6, 2026
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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.

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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.
This paper addresses the complexities of entanglement distribution in LEO satellite networks, particularly those arising from their dynamic topology. Traditional static and dynamic entanglement distribution methods often result in high entanglement drop rates and reduced end-to-end throughput. We introduce a novel framework that leverages the dynamic nature of LEO satellite networks to enhance entanglement distribution efficiency. Employing a space-time graph model to represent the network's temporal evolution, we propose an entanglement distribution strategy based on path utility, incorporating pointing errors, non-ideal link transmittance for intersatellite links, and atmospheric effects for downlinks. Our approach demonstrates superior performance in reducing entanglement drop rates and improving throughput compared to conventional methods. This study advances the field of quantum communication in satellite networks, offering resilient and efficient entanglement distribution strategies that support practical applications such as distributed computing, quantum multipartite cryptography, and distributed quantum sensing. The findings underscore the potential of integrating dynamic satellite networks with quantum technologies to create a reliable and secure quantum internet.
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The expansion of satellite-based quantum networks requires adaptive routing mechanisms that can sustain entanglement under dynamic orbital and atmospheric conditions. Conventional schemes, often tailored to static or idealised topologies, fail to capture the combined effects of orbital motion, fading, and trust variability in inter-satellite links. This work proposes an \textit{adaptive entanglement-aware routing framework} that jointly accounts for orbital geometry, atmospheric attenuation, and multi-parameter link evaluation. The routing metric integrates fidelity, trust, and key-rate weights to maintain connectivity and mitigate loss from turbulence and fading. Monte Carlo simulations across multiple orbital densities (ρ=10−6ρ= 10^{-6}ρ=10−6~km−3^{-3}−3) and environmental regimes, standard atmosphere, strong turbulence, and clear-sky LEO show up to a 275\% improvement in key generation rate and a 15\% increase in effective entanglement fidelity over existing adaptive methods. The framework achieves sub-linear path-length scaling with network size and remains robust for fading variances up to σfade=0.1σ_{\mathrm{fade}}=0.1σfade​=0.1, demonstrating strong potential for future global quantum constellations.
Timely availability of high-fidelity entanglement is essential for emerging quantum networks. This paper introduces the Age of Entanglement (AoE) as a novel performance metric that captures the freshness of bipartite entanglement under continuous distribution in quantum repeater chains. AoE extends classical Age of Information (AoI) based metrics to quantum networking by capturing storage, decoherence, probabilistic entanglement generation and swapping. We study a satellite-assisted quantum repeater network in which entangled pairs are generated probabilistically, stored in quantum memories suffer from decoherence, and combined to form end-to-end entangled links. Satellite-ground connectivity is intermittent and modeled as a two-state Markov chain. The resulting AoE minimization problem is formulated as an infinite-horizon Markov decision process (MDP), where control actions determine when to generate, store, or swap entangled pairs under stochastic link availability and memory degradation. Using relative value iteration, we characterize AoE-optimal policies and evaluate their performance numerically. Our results highlight the impact of decoherence, imperfect operations, and visibility dynamics, and show that the proposed dynamic policies significantly outperform swap-as-soon-as-possible and greedy entanglement generation strategies. Our results provide practical design and control guidelines for satellite-enabled quantum repeater chains supporting continuous entanglement distribution.
Establishing information-theoretically secure communication between arbitrary locations on Earth is a central goal of quantum networking, for which space-based distribution of quantum entanglement is a leading approach. Modelling and analysis of the performance of satellite entanglement pair distribution is therefore important for the architecture and design of future constellations and space systems. However, entanglement-based quantum key distribution in the absence of quantum repeaters, is especially prone to finite-key effects due to low coincident count rates compared to trusted-node single-path links. Quantifying these effects under realistic orbital conditions is therefore essential for the design of practical satellite quantum communication systems. Here, we develop a high-fidelity model of pair distribution from a low-Earth-orbit satellite that captures orbital dynamics, elevation-dependent loss, background noise, and extraneous detector effects. Integrating this with a finite-key security framework for the BBM92 protocol, we optimise the secret key length across different overpass geometries, orbital altitudes, and optical ground station (OGS) separations. We show that secure key generation remains feasible in early clear daytime conditions using baseline parameters representative of current technologies, while showing that modest system improvements could further extend daytime operation. Finally, we evaluate the annual secret key performance for representative intercity-scale OGS pairings. Our results provide quantitative performance bounds and practical design guidelines for near-term entanglement-based satellite QKD, enabling informed trade-offs between satellite payload complexity, ground infrastructure, and achievable secure key throughput.
Low Earth Orbit (LEO) satellites present a compelling opportunity for the establishment of a global quantum information network. However, satellite-based entanglement distribution from a networking perspective has not been fully investigated. Existing works often do not account for satellite movement over time when distributing entanglement and/or often do not permit entanglement distribution along inter-satellite links, which are two shortcomings we address in this paper. We first define a system model which considers both satellite movement over time and inter-satellite links. We next formulate the optimal entanglement distribution (OED) problem under this system model and show how to convert the OED problem in a dynamic physical network to one in a static logical graph which can be used to solve the OED problem in the dynamic physical network. We then propose a polynomial time greedy algorithm for computing satellite-assisted multi-hop entanglement paths. We also design an integer linear programming (ILP)-based algorithm to compute optimal solutions as a baseline to study the performance of our greedy algorithm. We present evaluation results to demonstrate the advantage of our model and algorithms.