Quantum key distribution (QKD) offers information-theoretic security for communication, superior to computationally secure methods vulnerable to quantum computers. Metropolitan-scale QKD systems exist, but building a global quantum internet (QI) faces significant challenges. Entanglement distribution, crucial for QI applications like quantum teleportation and distributed quantum computing, relies on single-photon qubits transmitted through the atmosphere or optical fibers. These methods suffer from exponential loss with distance. Quantum repeaters, although theoretically capable of overcoming this, require currently unattainable resources and have limited experimental demonstration. Satellites offer an advantage: most of the optical path is in free space, minimizing loss. They also facilitate long-distance QKD with untrusted nodes. This paper analyzes a global-scale QI architecture using a constellation of satellites in polar orbits to distribute entanglement to ground stations, which then connect via shorter ground-based links. The authors address key questions: the optimal number of satellites for continuous global coverage, their optimal altitude, and the achievable entanglement-distribution rates compared to ground-based quantum repeater schemes.

The paper reviews existing literature on quantum key distribution (QKD), highlighting the limitations of current ground-based systems for establishing a global quantum network. It discusses the advantages of satellite-based quantum communication, emphasizing reduced attenuation of optical signals in free space compared to atmospheric or fiber-optic links. Previous proposals for satellite-based quantum networks are mentioned, including those using satellite-to-ground, ground-to-satellite, or both transmission methods. The authors acknowledge recent experiments demonstrating satellite-based quantum communication but point out the lack of comprehensive analysis on the optimal configuration for a global-scale network.

The authors propose a satellite network architecture with *N*_R equally spaced rings of satellites in polar orbits, each ring having *N*_S equally spaced satellites at altitude *h*. The satellites act as entanglement sources, transmitting entangled photon pairs to ground stations. Entanglement is extended over longer distances via entanglement swapping at the ground stations, which act as quantum repeaters. The study focuses on downlinks only, avoiding the higher loss associated with uplinks. Simulations are conducted to determine optimal satellite configurations for continuous global coverage, considering the trade-off between the number of satellites and entanglement-distribution rates. A figure of merit, the ratio of the average entanglement-distribution rate to the total number of satellites (ebits/s per satellite), is defined and maximized. Simulations consider two ground stations at the equator, varying their separation distance *d* and satellite configurations. The loss model includes atmospheric attenuation, assuming clear skies. The influence of background photons is discussed, highlighting the challenge they pose to continuous global coverage. The simulation methodology incorporates a strategy for assigning satellites to ground station pairs, favoring those with the lowest loss. The methodology is extended to multiple ground stations, arranged in a grid-like configuration. A comparison is made with ground-based quantum repeater schemes using the formula of the rate $R_{M, N_{mem}} = rac{C N_{mem}}{2(d/M) W_{M, N_{mem}}}$, where M is the number of elementary links, N_{mem} is the number of quantum memories per repeater half-node, and $W_{M, N_{mem}}$ is the expected waiting time until one end-to-end pair is obtained.

Simulations reveal that increasing satellite altitude initially reduces the total number of satellites needed for continuous coverage, but beyond a certain altitude, the required number increases. An optimal altitude exists that minimizes the number of satellites while maintaining continuous coverage and acceptable loss. The optimal number of satellites and their altitude are determined for various ground station separations. Entanglement-distribution rates are found to exhibit an oscillatory behavior, peaking when satellites are closest to the ground stations. For two ground stations at the equator, the optimal entanglement-distribution rates decrease with increasing distance. For a constellation of 400 satellites, entanglement distribution at a reasonably high rate is not possible beyond approximately 7500 km. When considering multiple ground stations, loss is lowest for stations far from the equator. For a constellation of 225 satellites, entanglement-distribution rates vary across the grid of ground stations, with higher rates for those farther from the equator. Simulation results for entanglement distribution between major global cities (with a 400-satellite constellation) indicate that distances beyond 7500 km are challenging with the current configuration. A comparison with ground-based quantum repeater schemes shows that satellite-based schemes (without quantum repeaters) can outperform them in certain cases, particularly for shorter distances, though higher rates are achievable with ground-based repeaters with sufficient resources and high-coherence-time quantum memories. The fidelity of the transmitted entangled pairs is analyzed considering the presence of background photons, revealing a strong dependence on spectral irradiance and the feasibility of daytime operation for long distances.

The findings suggest that satellite-based entanglement distribution offers a viable approach to building a global-scale quantum internet, especially in the near term, due to the lower loss in free space and the current limitations of quantum memories for ground-based quantum repeaters. The authors acknowledge the limitations of their study, such as the assumption of clear skies, the use of a simplified loss model and the simplified treatment of the background noise. The results suggest that optimizing satellite constellations considering both the number of satellites and entanglement-distribution rates is crucial for building an efficient global quantum internet. The comparison with ground-based repeaters highlights the trade-off between achievable rates and technological readiness. While high-coherence-time quantum memories are needed for high rates with ground-based repeaters, the cost and availability of these memories are constraints.

The study provides a comprehensive analysis of a satellite-based architecture for a global quantum internet. It introduces a figure of merit for optimizing satellite configurations and presents simulations showing the trade-offs between satellite numbers, altitude, and entanglement distribution rates. The comparison with ground-based quantum repeaters highlights the near-term viability of satellite-based solutions. Future research should consider more realistic scenarios, incorporating factors such as weather conditions and developing more sophisticated assignment strategies for satellite-ground station pairings. Exploration of alternative satellite constellations and efficient routing algorithms is also warranted.

The simulations assume clear skies, neglecting the impact of weather conditions on atmospheric attenuation. The background noise model is a simplified approximation, not accounting for all potential sources of noise or dynamic changes. The entanglement distribution rates assume a simplified scenario without multimode transmission from satellites or multimode quantum memories at ground stations. The analysis focuses on a specific type of satellite constellation; other constellations might offer different performance characteristics. The assignment strategy for satellites to ground-station pairs is also simplified; more sophisticated algorithms could improve performance. The study's comparison to ground-based repeaters assumes ideal quantum memories with infinite coherence times, which is not realistic.