pith. machine review for the scientific record. sign in

arxiv: 2605.02164 · v1 · submitted 2026-05-04 · 🪐 quant-ph

Recognition: 3 theorem links

· Lean Theorem

Designing a Satellite Serviced Quantum Network Backbone for Concurrent Global Connectivity

Prateek Mantri , Stav Haldar , Albert Williams , Don Towsley
Authors on Pith no claims yet

Pith reviewed 2026-05-08 19:06 UTC · model grok-4.3

classification 🪐 quant-ph
keywords satellite quantum networksentanglement distributionLEO constellationsground station architecturetime-to-connectivitymulti-hop quantum pathsquantum backbonesatellite service policies
0
0 comments X

The pith

Anisotropic ground stations, multi-inclination orbits, and multi-party policies reduce time-to-connectivity in satellite quantum networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Satellite quantum networks require simultaneous multi-hop entanglement paths because quantum states cannot be copied and near-term devices have short buffering times. The authors simulate a backbone serving major global centers under waiting-time limits and identify three architectural improvements over simpler designs. Anisotropic ground-station placement shortens connectivity time by matching latitude-dependent satellite access, multi-inclination constellations provide better coverage for diverse latitudes at fixed satellite counts, and multi-party service policies ease per-satellite concurrency limits. Altitude stands out as the main physical control on the visibility versus loss trade-off. The results map out conditions for scalable concurrent entanglement distribution via satellites.

Core claim

Across a broad parameter sweep, anisotropic ground-station lattices reduce time-to-connectivity relative to longitudinally collapsed and isotropic baselines by aligning ground infrastructure with latitude-dependent satellite access. Multi-inclination LEO constellations reduce waiting times for strong connectivity compared to single-inclination constellations at fixed satellite budgets by providing additional visibility for a diverse latitude set. Multi-party satellite service policies alleviate per-satellite concurrency bottlenecks and substantially reduce time-to-connectivity at stringent traffic-matrix thresholds. Satellite altitude is the dominant physical lever shaping the visibility--f,

What carries the argument

Discrete-time simulator that evaluates time-to-connectivity and latency-conditioned average active-link strength by tracking visibility windows, finite waiting-time constraints, and per-satellite concurrency limits for a traffic matrix of major population and financial centers.

Load-bearing premise

The discrete-time simulator accurately captures the interplay of visibility windows, finite waiting-time constraints, and per-satellite concurrency limits under the chosen traffic matrix of major population and financial centers.

What would settle it

Measure actual time-to-connectivity and active-link strength in a deployed small-scale satellite quantum testbed with anisotropic ground stations and multi-inclination orbits, then compare against simulator output for identical parameters and traffic matrix.

Figures

Figures reproduced from arXiv: 2605.02164 by Albert Williams, Don Towsley, Prateek Mantri, Stav Haldar.

Figure 1
Figure 1. Figure 1: Schematic illustration of the orbital parameters governing satellite-serviced network geometry. Satellites are arranged in inclined orbital planes distinguished by their right ascension of the ascending node (RAAN), which sets the longitudinal orientation of each plane. Within a plane, satellites are separated by in-plane phase offsets that determine along-track spacing and revisit times. Orbital altitude … view at source ↗
Figure 2
Figure 2. Figure 2: Snapshot of bipartite connectivity (ebits delivered per unit time) for a ground-station grid with 176 stations across North America and Western Europe. The constellation consists of satellites at an altitude of 500 km, arranged in 360 orbital planes with 18 satellites per plane. Ninety percent of planes form a primary shell at inclination 53◦ , with the remainder allocated to a secondary polar shell. Groun… view at source ↗
Figure 3
Figure 3. Figure 3: Ground-station density induced by the anisotropy parameter α. (a) Schematic illustrations of candidate spherical lattice layouts for different values of the anisotropy parameter α, showing how increasing α progressively suppresses excessive high-latitude longitudinal densification. (b) Relative longitudinal ground￾station density as a function of latitude λ and anisotropy parameter α, with colors showing l… view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of a hub–spoke–ring service model for a satellite-serviced quantum backbone. During each satellite pass, the satellite designates a sin￾gle ground station as a hub (nearest visible station) and services a fixed local neighborhood consisting of the hub and its six nearest terrestrial neighbors. En￾tanglement distribution is restricted to hub–spoke links and ring links among the neighboring stat… view at source ↗
Figure 5
Figure 5. Figure 5: Geometry of the satellite-to-ground op￾tical channel. A diffraction-limited Gaussian beam of waist w0 is emitted from the satellite, experiences atmo￾spheric loss given by ηatm, and free-space diffraction loss given by ηgeo, and is partially collected by the ground￾station receiver aperture. Pointing error arising from satellite jitter and tracking inaccuracy is represented by a lateral displacement of the… view at source ↗
Figure 6
Figure 6. Figure 6: Illustrative time series of the instanta￾neous largest connected component (LCC) frac￾tion over a representative thirty-minute window of the satellite-serviced ground-station graph(see Sec. 3.3 and Appendix B.2 for details). The trace shows quasi-periodic reductions in concurrent connec￾tivity caused by time-varying satellite–ground visibility. These low-connectivity intervals motivate the forward￾wait met… view at source ↗
Figure 7
Figure 7. Figure 7: City grid used to construct the traffic matrix. Blue markers denote global financial centers, while red markers denote major population hubs not included in the financial centers list. Together, these cities provide broad geographic coverage across continents and regions and serve as application-relevant endpoints for evaluating backbone connectivity. 3.1.2 Latency conditioned average link strength Connect… view at source ↗
Figure 8
Figure 8. Figure 8: Satellite budget–latency tradeoffs for traffic-matrix connectivity under different ground￾station geometries. Curves correspond to longitudinal (α = −1), isotropic (α = 0), and anisotropic (α > 0) ground-station grids. Shaded regions indicate ±1 standard error over simulation realizations. (a) Mean waiting time to achieve fixed global connectivity thresholds (50%, and 100% of city pairs connected) as a fun… view at source ↗
Figure 9
Figure 9. Figure 9: Average latency-conditioned active-link strength as a function of the required traffic￾matrix connectivity threshold ϑ, under different satellite budgets. The three panels restrict the design search to constellations with at most 1250, 2500, and 5000 satellites, respectively. For each threshold, the plot￾ted value is the best average active-link strength achieved among configurations satisfying the satelli… view at source ↗
Figure 10
Figure 10. Figure 10: Minimum mean waiting time required to satisfy concurrent traffic-matrix connectivity targets for augmented dual-shell (ADS) and single-shell (SS) constellations. Purple curves denote ADS constellations and orange curves denote SS constellations. All plotted configurations are restricted to satellite service concurrency T = 7, ensuring that the comparison isolates constellation architecture rather than per… view at source ↗
Figure 11
Figure 11. Figure 11: Average latency-conditioned active-link strength for augmented dual-shell (ADS) and single-shell (SS) constellation designs, evaluated at different concurrent traffic-matrix connectiv￾ity thresholds ϑ. The three panels condition the design search on total satellite budgets of 1250, 2500, and 5000 satellites, respectively. Purple curves denote ADS constellations and orange curves denote SS constella￾tions.… view at source ↗
Figure 12
Figure 12. Figure 12: , increasing T under a fixed total terminal budget sharply reduces the wait time needed to achieve full traffic-matrix connectivity, especially for anisotropic ground-station layouts view at source ↗
Figure 13
Figure 13. Figure 13: Mean wait time to achieve global connectivity under bi-partite (BPC) and multi-party (MPC) satellite operation. (a) Minimum mean wait time W required to achieve full connectivity (ϑ = 100%) as a function of satellite budget. (b)–(d) Mean wait time as a function of the connectivity threshold ϑ for fixed satellite budgets of 1250, 2500, and 5000 satellites, respectively. Curves compare bi-partite connectivi… view at source ↗
Figure 14
Figure 14. Figure 14: shows that MPC maintains a latency advantage at high connectivity thresholds even when plotted against total terminal budget, indicating that the gains are not explained solely by increased terminal count but also by increased degree of the graph formed on the ground station grid view at source ↗
Figure 15
Figure 15. Figure 15: Latency-conditioned average active-link strength under bi-partite (BPC) and multi￾party (MPC) connectivity. Average active-link strength as a function of the connectivity threshold ϑ for fixed terminal budgets of 5000, 10000, and 15000, shown in (a)–(c), respectively. Curves compare multi-party connectivity (MPC, purple) and bi-partite connectivity (BPC, orange). At stringent connectivity thresholds, BPC … view at source ↗
Figure 16
Figure 16. Figure 16: Mean wait time as a function of total satellite budget for different satellite altitudes and connectivity thresholds. Panels (a), and (b) correspond to constellations with 120 and 240 orbital planes, respectively, shown as representative plane counts. The first and third plots correspond to ϑ ≥ 50%, while the second and fourth plots correspond to ϑ = 100%. Colors indicate different satellite altitudes, wi… view at source ↗
Figure 17
Figure 17. Figure 17: Effect of orbital-plane count and satellite altitude on connectivity latency and average link strength. Panel (a) shows the mean wait time required to reach a specified city–city connectivity threshold ϑ, while panel (b) shows the corresponding latency-conditioned average active-link strength for Wmax = 1 s. The first and third plots correspond to ϑ ≥ 50%, while the second and fourth plots correspond to ϑ… view at source ↗
Figure 18
Figure 18. Figure 18: Effect of orbital-plane count and satellites per orbital plane on connectivity latency and link quality. Panel (a) shows the mean wait time required to reach a specified city–city connectivity threshold ϑ, while panel (b) shows the corresponding latency-conditioned average active-link strength for Wmax = 1 s. The first and third plots correspond to ϑ ≥ 50%, while the second and fourth plots correspond to … view at source ↗
read the original abstract

Satellite-serviced quantum networks pose an architectural problem distinct from classical satellite networking: because entanglement cannot be copied, and long-lived buffering is technologically constrained for near-term devices, useful end-to-end service requires fixed optical ground infrastructure and simultaneous multi-hop path availability. We investigate the design of a satellite-serviced quantum backbone aimed at supporting concurrent global connectivity across a traffic matrix of major population and financial centers under finite waiting-time constraints. Using a discrete-time simulator, we evaluate performance using two architecture-level metrics: (i) time-to-connectivity, and (ii) latency-conditioned average active-link strength. Across a broad parameter sweep, we identify three dominant architectural effects. First, anisotropic ground-station lattices reduce time-to-connectivity relative to longitudinally collapsed and isotropic baselines by aligning ground infrastructure with latitude-dependent satellite access. Second, multi-inclination LEO constellations reduce waiting times for strong connectivity compared to single-inclination constellations at fixed satellite budgets by providing additional visibility for a diverse latitude set. Third, multi-party satellite service policies alleviate per-satellite concurrency bottlenecks and substantially reduce time-to-connectivity at stringent traffic-matrix thresholds. We further show that satellite altitude is the dominant physical lever shaping the visibility--loss trade-off, strongly affecting both connectivity latency and achievable link strength, while orbital plane count and satellite packing provide secondary refinements at fixed altitude. Together, these results delineate the architectural conditions required for scalable, concurrent entanglement connectivity in satellite-serviced quantum networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The paper uses a discrete-time simulator to study the design of a satellite-serviced quantum network backbone supporting concurrent global entanglement connectivity under finite waiting-time constraints and a fixed traffic matrix of major population/financial centers. It defines two architecture-level metrics—time-to-connectivity and latency-conditioned average active-link strength—and reports three dominant effects from parameter sweeps: (1) anisotropic ground-station lattices reduce time-to-connectivity relative to isotropic or longitudinally collapsed baselines by better aligning with latitude-dependent satellite visibility; (2) multi-inclination LEO constellations reduce waiting times for strong connectivity at fixed satellite budgets; (3) multi-party satellite service policies alleviate per-satellite concurrency limits and substantially improve performance at stringent traffic thresholds. Satellite altitude is identified as the dominant physical lever via the visibility-loss trade-off, with orbital plane count and packing as secondary factors.

Significance. If the simulator faithfully captures the interplay of visibility windows, concurrency limits, and waiting-time constraints, the results would offer concrete, actionable guidance for near-term quantum network architecture, emphasizing latitude-aware ground infrastructure and flexible service policies over simpler isotropic or single-inclination designs. The work addresses a genuine architectural distinction arising from the no-cloning theorem and limited quantum memory, and the parameter-sweep approach provides falsifiable predictions that could be tested against future hardware deployments.

major comments (3)
  1. [§4] §4 (Simulator description): The central claims rest entirely on simulation outputs, yet the manuscript provides neither the explicit update rules for visibility windows, per-satellite concurrency, nor the precise parameter values and ranges used in the sweeps. Without these, it is impossible to determine whether the reported dominance of the three architectural effects is robust or an artifact of unstated modeling choices (e.g., the exact form of the waiting-time constraint or the traffic-matrix threshold definition).
  2. [§5.2–5.3] §5.2–5.3 (Results on multi-inclination and multi-party policies): The claim that multi-inclination constellations and multi-party policies “substantially reduce” time-to-connectivity is load-bearing for the paper’s architectural recommendations, but no sensitivity analysis is shown with respect to the chosen traffic matrix or the precise definition of “strong connectivity.” A single additional figure or table varying the matrix or threshold would be required to establish that the effect is not an artifact of the specific external traffic pattern.
  3. [§3] §3 (Metric definitions): The latency-conditioned average active-link strength metric is introduced without an explicit formula or pseudocode. Because this metric is used to quantify the second and third effects, its precise construction (including how latency conditioning is applied and how “active” links are counted) must be stated mathematically before the quantitative comparisons can be evaluated.
minor comments (3)
  1. [Abstract / §1] The abstract and introduction use the term “anisotropic ground-station lattices” without a concise definition or reference to the exact latitude/longitude placement rule; a one-sentence clarification would improve readability.
  2. [Figures 3–6] Figure captions for the parameter-sweep plots should explicitly state the fixed values of all other parameters (satellite budget, altitude, etc.) so that each panel can be interpreted independently.
  3. [§4] A short discussion of computational complexity or run-time of the discrete-time simulator would help readers assess the feasibility of extending the study to larger constellations or finer time steps.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We have revised the manuscript to address all major comments by adding the requested details on the simulator, metric definitions, and sensitivity analyses. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [§4] §4 (Simulator description): The central claims rest entirely on simulation outputs, yet the manuscript provides neither the explicit update rules for visibility windows, per-satellite concurrency, nor the precise parameter values and ranges used in the sweeps. Without these, it is impossible to determine whether the reported dominance of the three architectural effects is robust or an artifact of unstated modeling choices (e.g., the exact form of the waiting-time constraint or the traffic-matrix threshold definition).

    Authors: We agree that the original §4 lacked sufficient implementation details for reproducibility. The revised manuscript expands this section with explicit update rules for visibility windows and per-satellite concurrency, plus a table enumerating all parameter values and ranges from the sweeps. These additions enable independent verification of the reported architectural effects. revision: yes

  2. Referee: [§5.2–5.3] §5.2–5.3 (Results on multi-inclination and multi-party policies): The claim that multi-inclination constellations and multi-party policies “substantially reduce” time-to-connectivity is load-bearing for the paper’s architectural recommendations, but no sensitivity analysis is shown with respect to the chosen traffic matrix or the precise definition of “strong connectivity.” A single additional figure or table varying the matrix or threshold would be required to establish that the effect is not an artifact of the specific external traffic pattern.

    Authors: We have conducted the requested sensitivity analyses. The revised manuscript includes a new figure showing that the performance gains from multi-inclination constellations and multi-party policies remain consistent across alternative traffic matrices and varied thresholds for strong connectivity. This confirms the robustness of the architectural recommendations. revision: yes

  3. Referee: [§3] §3 (Metric definitions): The latency-conditioned average active-link strength metric is introduced without an explicit formula or pseudocode. Because this metric is used to quantify the second and third effects, its precise construction (including how latency conditioning is applied and how “active” links are counted) must be stated mathematically before the quantitative comparisons can be evaluated.

    Authors: We have added an explicit mathematical definition and pseudocode for the latency-conditioned average active-link strength metric to the revised §3. This specifies the latency conditioning procedure and the criteria for counting active links, allowing direct evaluation of the quantitative comparisons. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents results from a discrete-time simulator comparing architectural variants (anisotropic lattices, multi-inclination constellations, multi-party policies) against fixed external inputs: a traffic matrix of population/financial centers, physical visibility windows, and concurrency constraints. The two metrics—time-to-connectivity and latency-conditioned average active-link strength—are defined independently of the tested configurations and are not fitted or renamed from simulation outputs. No equations, first-principles derivations, or predictions are shown that reduce by construction to the inputs; the three dominant effects are direct consequences of running the same simulator across parameter sweeps. No load-bearing self-citations or ansatz smuggling appear in the abstract or description. The derivation chain is therefore self-contained against the stated modeling assumptions.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The claims rest on a discrete-time simulator whose internal timing, loss, and concurrency models are not detailed in the abstract; the traffic matrix and waiting-time thresholds are treated as given inputs.

free parameters (3)
  • satellite budget
    Fixed total number of satellites used across single- and multi-inclination constellations
  • ground-station lattice geometry
    Parameters defining anisotropic, isotropic, and longitudinally collapsed layouts
  • satellite altitude
    Primary physical parameter varied to trade visibility against loss
axioms (2)
  • domain assumption Entanglement cannot be copied
    Standard quantum information constraint invoked to require simultaneous multi-hop paths
  • domain assumption Long-lived quantum buffering is technologically constrained for near-term devices
    Justifies the finite waiting-time constraint in the simulator

pith-pipeline@v0.9.0 · 5562 in / 1416 out tokens · 81556 ms · 2026-05-08T19:06:46.038881+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

77 extracted references · 23 canonical work pages

  1. [1]

    Satellite quantum communications: Fundamental bounds and practical security,

    S. Pirandola, “Satellite quantum communications: Fundamental bounds and practical security,”Physical Review Research, vol. 3, no. 2, p. 023130, May 2021, publisher: American Physical Society. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevResearch.3.023130

    work page doi:10.1103/physrevresearch.3.023130 2021

  2. [2]

    On approaching the ultimate limits of photon- efficient and bandwidth-efficient optical communication,

    S. Dolinar, K. M. Birnbaum, B. I. Erkmen, and B. Moision, “On approaching the ultimate limits of photon- efficient and bandwidth-efficient optical communication,”2011 International Conference on Space Optical Systems and Applications (ICSOS), pp. 269–278, Jun. 2011

    2011

  3. [3]

    Satellite-based entanglement distribution over 1200 kilometers,

    J. Yin, Y. Cao, Y.-H. Li, S.-K. Liao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, B. Li, H. Daiet al., “Satellite-based entanglement distribution over 1200 kilometers,”Science, vol. 356, no. 6343, pp. 1140–1144, 2017

    2017

  4. [4]

    Entanglement-based secure quantum cryptography over 1,120 kilometres,

    J. Yin, Y.-H. Li, S.-K. Liao, M. Yang, Y. Cao, L. Zhang, J.-G. Ren, W.-Q. Cai, W.-Y. Liu, S.-L. Li, R. Shu, Y.-M. Huang, L. Deng, L. Li, Q. Zhang, N.-L. Liu, Y.-A. Chen, C.-Y. Lu, X.-B. Wang, F. Xu, J.-Y. Wang, C.-Z. Peng, A. K. Ekert, and J.-W. Pan, “Entanglement-based secure quantum cryptography over 1,120 kilometres,”Nature, vol. 582, pp. 501–505, 2020

    2020

  5. [5]

    Ground-to-satellite quantum teleportation,

    J.-G. Ren, P. Xu, H.-L. Yong, L. Zhang, S.-K. Liao, J. Yin, W.-Y. Liu, W.-Q. Cai, M. Yang, L. Li, K.-X. Yang, X. Han, Y.-Q. Yao, J. Li, H.-Y. Wu, S. Wan, L. Liu, D.-Q. Liu, Y.-W. Kuang, Z.-P. He, P. Shang, C. Guo, R.-H. Zheng, K. Tian, Z.-C. Zhu, N.-L. Liu, C.-Y. Lu, R. Shu, Y.-A. Chen, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Ground-to-satellite quantum t...

    2017

  6. [6]

    Towards satellite-based quantum-secure time transfer,

    H. Dai, Q. Shen, C.-Z. Wang, S.-L. Li, W.-Y. Liu, W.-Q. Cai, S.-K. Liao, J.-G. Ren, J. Yin, Y.-A. Chen, Q. Zhang, F. Xu, C.-Z. Peng, and J.-W. Pan, “Towards satellite-based quantum-secure time transfer,” Nature Physics, vol. 16, pp. 848–852, 2020

    2020

  7. [7]

    Satellites promise global-scale quantum networks,

    S. Goswami, S. Dhara, N. Sinclair, M. Mohageg, J. S. Sidhu, S. Mukhopadhyay, M. Krutzik, J. R. Lowell, D. K. Oi, M. Gündoğanet al., “Satellites promise global-scale quantum networks,”Optica Quantum, vol. 3, no. 6, pp. 590–605, 2025

    2025

  8. [8]

    Ultrafast and fault-tolerant quantum communication across long distances,

    S. Muralidharan, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang, “Ultrafast and fault-tolerant quantum communication across long distances,”Physical review letters, vol. 112, no. 25, p. 250501, 2014

    2014

  9. [9]

    Rate-loss analysis of an efficient quantum repeater architecture,

    S. Guha, H. Krovi, C. A. Fuchs, Z. Dutton, J. A. Slater, C. Simon, and W. Tittel, “Rate-loss analysis of an efficient quantum repeater architecture,”Physical Review A, vol. 92, no. 2, p. 022357, 2015

    2015

  10. [10]

    Optimal architectures for long distance quantum communication,

    S. Muralidharan, L. Li, J. Kim, N. Lütkenhaus, M. D. Lukin, and L. Jiang, “Optimal architectures for long distance quantum communication,”Scientific Reports, vol. 6, no. 1, p. 20463, Apr. 2016. [Online]. Available: http://www.nature.com/articles/srep20463 1

    2016

  11. [11]

    Comparingone-andtwo-wayquantumrepeaterarchitectures,

    P.Mantri, K.Goodenough, andD.Towsley, “Comparingone-andtwo-wayquantumrepeaterarchitectures,” Communications Physics, vol. 8, no. 1, p. 30, 2025

    2025

  12. [12]

    Satellite-mediated quantum atmospheric links,

    D. Vasylyev, W. Vogel, and F. Moll, “Satellite-mediated quantum atmospheric links,”Physical Review A, vol. 99, no. 5, May 2019. [Online]. Available: https://doi.org/10.1103/physreva.99.053830

    work page doi:10.1103/physreva.99.053830 2019

  13. [13]

    Advances in space quantum communications,

    J.S.Sidhu, S.K.Joshi, M.Gündoğan, T.Brougham, D.Lowndes, L.Mazzarella, M.Krutzik, S.Mohapatra, D. Dequal, G. Valloneet al., “Advances in space quantum communications,”IET Quantum Communication, vol. 2, no. 4, pp. 182–217, 2021

    2021

  14. [14]

    Bell’s shadows from satellites,

    S. Haldar, R. L. McDonald, S. Ducoing, and I. Agullo, “Bell’s shadows from satellites,”arXiv preprint arXiv:2412.13416, 2024

    work page arXiv 2024

  15. [15]

    Satellite-Relayed Global Quantum Communication without Quantum Memory,

    S. Goswami and S. Dhara, “Satellite-Relayed Global Quantum Communication without Quantum Memory,”Physical Review Applied, vol. 20, no. 2, p. 024048, Aug. 2023. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevApplied.20.024048

    work page doi:10.1103/physrevapplied.20.024048 2023

  16. [16]

    Optical ground station diversity for satellite quantum key distribution in ireland,

    N. L. Anipeddi, J. Horgan, D. K. Oi, and D. Kilbane, “Optical ground station diversity for satellite quantum key distribution in ireland,”EPJ Quantum Technology, vol. 12, no. 1, p. 91, 2025

    2025

  17. [17]

    Quantum time transfer for freespace quantum networking,

    R. Lafler and R. N. Lanning, “Quantum time transfer for freespace quantum networking,” 2022. [Online]. Available: https://arxiv.org/abs/2211.00737

    work page arXiv 2022

  18. [18]

    Spooky action at a global distance: analysis of space-based entanglement distribution for the quantum internet,

    S. Khatri, A. J. Brady, R. A. Desporte, M. P. Bart, and J. P. Dowling, “Spooky action at a global distance: analysis of space-based entanglement distribution for the quantum internet,”npj Quantum Information, vol. 7, no. 1, p. 4, Jan. 2021, publisher: Nature Publishing Group. [Online]. Available: https://www.nature.com/articles/s41534-020-00327-5

    2021

  19. [19]

    Connecting quantum cities: simulation of a satellite-based quantum network,

    R. Yehia, M. Schiavon, V. Marulanda Acosta, T. Coopmans, I. Kerenidis, D. Elkouss, and E. Diamanti, “Connecting quantum cities: simulation of a satellite-based quantum network,” New Journal of Physics, vol. 26, no. 7, p. 073015, Jul. 2024. [Online]. Available: https: //iopscience.iop.org/article/10.1088/1367-2630/ad5b13

    work page doi:10.1088/1367-2630/ad5b13 2024

  20. [20]

    Hybrid satellite-fiber quantum network,

    Y. Shao, S. Guha, and A. E. Motter, “Hybrid satellite-fiber quantum network,” Jul. 2025, arXiv:2507.12539 [quant-ph]. [Online]. Available: http://arxiv.org/abs/2507.12539

    work page arXiv 2025

  21. [21]

    Handover schemes in satellite networks: State- of-the-art and future research directions

    P. K. Chowdhury, M. Atiquzzaman, W. D. Ivancicet al., “Handover schemes in satellite networks: State- of-the-art and future research directions.”IEEE Commun. Surv. Tutorials, vol. 8, no. 1-4, pp. 2–14, 2006

    2006

  22. [22]

    A user-centric handover scheme for ultra-dense leo satellite networks,

    J. Li, K. Xue, J. Liu, and Y. Zhang, “A user-centric handover scheme for ultra-dense leo satellite networks,” IEEE Wireless Communications Letters, vol. 9, no. 11, pp. 1904–1908, 2020

    1904

  23. [23]

    Survey on optimization methods for leo-satellite-based networks with applications in future autonomous transportation,

    K. Çelikbilek, Z. Saleem, R. Morales Ferre, J. Praks, and E. S. Lohan, “Survey on optimization methods for leo-satellite-based networks with applications in future autonomous transportation,”Sensors, vol. 22, no. 4, p. 1421, 2022

    2022

  24. [24]

    Handover technique in leo satellite networks: A review,

    Z. Liu, Z. Yang, G. Pan, H. Zhang, G. Luo, and H. Yang, “Handover technique in leo satellite networks: A review,” in2024 13th International Conference on Communications, Circuits and Systems (ICCCAS). IEEE, 2024, pp. 364–369

    2024

  25. [25]

    Leotcp: Low-latency and high-throughput data transport for leo satellite networks,

    A. Valentine and G. Parisis, “Leotcp: Low-latency and high-throughput data transport for leo satellite networks,”arXiv preprint arXiv:2508.19067, 2025

    work page arXiv 2025

  26. [26]

    Ameasurementstudyofdynamicsandliquiddatatransport in oneweb leo satellite networks,

    O.Perrin, E.Gossling, D.Qiao, andH.Zhang, “Ameasurementstudyofdynamicsandliquiddatatransport in oneweb leo satellite networks,” inMILCOM 2025-2025 IEEE Military Communications Conference (MILCOM). IEEE, 2025, pp. 1–6. 2

    2025

  27. [27]

    A single quantum cannot be cloned,

    W. K. Wootters and W. H. Zurek, “A single quantum cannot be cloned,”Nature, vol. 299, no. 5886, pp. 802–803, 1982

    1982

  28. [28]

    Quantum repeaters based on single trapped ions,

    N. Sangouard, R. Dubessy, and C. Simon, “Quantum repeaters based on single trapped ions,”Physical Review A, vol. 79, no. 4, p. 042340, Apr. 2009. [Online]. Available: https: //link.aps.org/doi/10.1103/PhysRevA.79.042340

    work page doi:10.1103/physreva.79.042340 2009

  29. [29]

    Diamond nv centers for quantum computing and quantum networks,

    L. Childress and R. Hanson, “Diamond nv centers for quantum computing and quantum networks,”MRS Bulletin, vol. 38, no. 2, p. 134–138, 2013

    2013

  30. [30]

    Quantum repeaters based on atomic ensembles and linear optics

    N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, “Quantum repeaters based on atomic ensembles and linear optics,”Reviews of Modern Physics, vol. 83, no. 1, pp. 33–80, Mar. 2011. [Online]. Available: https://link.aps.org/doi/10.1103/RevModPhys.83.33

    work page doi:10.1103/revmodphys.83.33 2011

  31. [31]

    Fast quantum logic gates with trapped-ion qubits,

    V. M. Schäfer, C. J. Ballance, K. Thirumalai, L. Stephenson, T. Ballance, A. Steane, and D. Lucas, “Fast quantum logic gates with trapped-ion qubits,”Nature, vol. 555, no. 7694, pp. 75–78, 2018

    2018

  32. [32]

    Entanglement generation in a quantum network with finite quantum memory lifetime,

    V. Semenenko, X. Hu, E. Figueroa, and V. Perebeinos, “Entanglement generation in a quantum network with finite quantum memory lifetime,”AVS Quantum Science, vol. 4, no. 1, 2022

    2022

  33. [33]

    Quantum repeaters: From quantum networks to the quantum internet,

    K. Azuma, S. E. Economou, D. Elkouss, P. Hilaire, L. Jiang, H.-K. Lo, and I. Tzitrin, “Quantum repeaters: From quantum networks to the quantum internet,”Reviews of Modern Physics, vol. 95, no. 4, p. 045006, 2023

    2023

  34. [34]

    Effective routing design for remote entanglement generation on quantum networks,

    C. Li, T. Li, Y.-X. Liu, and P. Cappellaro, “Effective routing design for remote entanglement generation on quantum networks,”npj Quantum Information, vol. 7, no. 1, p. 10, 2021

    2021

  35. [35]

    Routing entanglement in the quantum internet,

    M. Pant, H. Krovi, D. Towsley, L. Tassiulas, L. Jiang, P. Basu, D. Englund, and S. Guha, “Routing entanglement in the quantum internet,”npj Quantum Information, vol. 5, no. 1, p. 25, Mar. 2019, publisher: Nature Publishing Group. [Online]. Available: https://www.nature.com/articles/s41534-019-0139-x

    2019

  36. [36]

    Satellite quantum communications: Fundamental bounds and practical security,

    S. Pirandola, “Satellite quantum communications: Fundamental bounds and practical security,”Physical Review Research, vol. 3, no. 2, p. 023130, 2021

    2021

  37. [37]

    Satellite-based photonic quantum networks are small-world,

    S. Brito, A. Canabarro, D. Cavalcanti, and R. Chaves, “Satellite-based photonic quantum networks are small-world,”Prx Quantum, vol. 2, no. 1, p. 010304, 2021

    2021

  38. [38]

    CubeSat Design Specification Revision 14,

    California-Polytechnic-State University, “CubeSat Design Specification Revision 14,” https://www.cubesat.org/cds-announcement, Last accessed: Dec. 26 2021

    2021

  39. [39]

    CubeSat quantum communications mission,

    D. K. Oi, A. Ling, G. Vallone, P. Villoresi, S. Greenland, E. Kerr, M. Macdonald, H. Weinfurter, H. Kuiper, E. Charbon, and R. Ursin, “CubeSat quantum communications mission,”EPJ Quantum Technology, vol. 4, no. 1, pp. 1–20, Dec. 2017, publisher: SpringerOpen. [Online]. Available: https://epjquantumtechnology.springeropen.com/articles/10.1140/epjqt/s40507-...

    work page doi:10.1140/epjqt/s40507-017-0060-1 2017

  40. [40]

    Entanglement demonstration on board a nano-satellite,

    A. Villar, A. Lohrmann, X. Bai, T. Vergoossen, R. Bedington, C. Perumangatt, H. Y. Lim, T. Islam, A. Reezwana, Z. Tang, R. Chandrasekara, S. Sachidananda, K. Durak, C. F. Wildfeuer, D. Griffin, D. K. L. Oi, and A. Ling, “Entanglement demonstration on board a nano-satellite,”Optica, vol. 7, p. 734, 2020

    2020

  41. [41]

    Fully on-chip photonic turnkey quantum source for entangled qubit/qudit state generation,

    H. Mahmudlu, R. Johanning, A. van Rees, A. Khodadad Kashi, J. P. Epping, R. Haldar, K.-J. Boller, and M. Kues, “Fully on-chip photonic turnkey quantum source for entangled qubit/qudit state generation,” Nature Photonics, vol. 17, no. 6, pp. 518–524, Jun. 2023, publisher: Nature Publishing Group. [Online]. Available: https://www.nature.com/articles/s41566-...

    2023

  42. [42]

    PRX Quantum5, 010102 (2024) https://doi.org/ 10.1103/PRXQuantum.5.010102

    S. Simmons, “Scalable Fault-Tolerant Quantum Technologies with Silicon Color Centers,”PRX Quantum, vol. 5, no. 1, p. 010102, Mar. 2024, publisher: American Physical Society. [Online]. Available: https://link.aps.org/doi/10.1103/PRXQuantum.5.010102 3

    work page doi:10.1103/prxquantum.5.010102 2024

  43. [43]

    On-Chip Quantum Interference between Independent Lithium Niobate-on-Insulator Photon-Pair Sources,

    R. J. Chapman, T. Kuttner, J. Kellner, A. Sabatti, A. Maeder, G. Finco, F. Kaufmann, and R. Grange, “On-Chip Quantum Interference between Independent Lithium Niobate-on-Insulator Photon-Pair Sources,” Physical Review Letters, vol. 134, no. 22, p. 223602, Jun. 2025, publisher: American Physical Society. [Online]. Available: https://link.aps.org/doi/10.1103...

    work page doi:10.1103/n2y3-2bmz 2025

  44. [44]

    Multiple Simultaneous Optical Links for Space-Based Platforms

    A. C. Aguilar, “Multiple Simultaneous Optical Links for Space-Based Platforms.”

  45. [45]

    using Laser Arrays for CubeSats in Low Earth Orbit (LEO) or Low Lunar Orbit (LLO)

    P. M. Goorjian, “using Laser Arrays for CubeSats in Low Earth Orbit (LEO) or Low Lunar Orbit (LLO).”

  46. [46]

    Starlink technology,

    SpaceX, “Starlink technology,” accessed January 2026. [Online]. Available: https://starlink.com/technology

    2026

  47. [47]

    Amazon Leo,

    “Amazon Leo,” https://www.aboutamazon.com/what-we-do/devices-services/amazon-leo

  48. [48]

    Scot20 - smallsat optical communication terminal,

    TESAT-Spacecom, “Scot20 - smallsat optical communication terminal,” 2024. [Online]. Available: https://www.tesat.de/products

    2024

  49. [49]

    Quantum internet protocol stack: A comprehensive survey,

    J. Illiano, M. Caleffi, A. Manzalini, and A. S. Cacciapuoti, “Quantum internet protocol stack: A comprehensive survey,”Computer Networks, vol. 213, p. 109092, Aug. 2022. [Online]. Available: https://doi.org/10.1016/j.comnet.2022.109092

    work page doi:10.1016/j.comnet.2022.109092 2022

  50. [50]

    An in-depth investigation of leo satellite topology design parameters,

    W. Zhang, Z. Xu, and S. A. Jyothi, “An in-depth investigation of leo satellite topology design parameters,” inProceedings of the 2nd International Workshop on LEO Networking and Communication, 2024, pp. 1–6

    2024

  51. [51]

    Optimal ground station selection for low-Earth orbiting satellites,

    D. Eddy, M. Ho, and M. J. Kochenderfer, “Optimal Ground Station Selection for Low-Earth Orbiting Satellites,” Mar. 2025, arXiv:2410.16282 [cs]. [Online]. Available: http://arxiv.org/abs/2410.16282

    work page arXiv 2025

  52. [52]

    Robust quantum network architectures and topologies for entanglement distribution,

    S. Das, S. Khatri, and J. P. Dowling, “Robust quantum network architectures and topologies for entanglement distribution,”Physical Review A, vol. 97, no. 1, p. 012335, Jan. 2018, publisher: American Physical Society. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.97.012335

    work page doi:10.1103/physreva.97.012335 2018

  53. [53]

    Global Financial Centres Index,

    “Global Financial Centres Index,” Aug. 2025, page Version ID: 1305535083. [Online]. Available: https://en.wikipedia.org/w/index.php?title=Global_Financial_Centres_Index&oldid=1305535083

    2025

  54. [54]

    The global satellite market is forecast to become seven times bigger

    “The global satellite market is forecast to become seven times bigger.” [Online]. Available: https://www. goldmansachs.com/insights/articles/the-global-satellite-market-is-forecast-to-become-seven-times-bigger

  55. [55]

    Free-space optical communications with multibeam laser terminals for satellites: design insights and applications,

    J. Spaander, R. Saathof, J. Guo, and E. Gill, “Free-space optical communications with multibeam laser terminals for satellites: design insights and applications,” inInternational Conference on Space Optics — ICSO 2024, vol. 13699. SPIE, Jul. 2025, pp. 2780–2804. [Online]. Available: https://www.spiedigitallibrary.org/conference-proceedings-of-spie/13699/1...

    work page doi:10.1117/12.3075401.full 2024

  56. [56]

    Supplementary materials,

    “Supplementary materials,” 2026. [Online]. Available: https://github.com/mantri-prateek/ Designing-a-Satellite-Serviced-Quantum-Network-Backbone-for-Concurrent-Global-Connectivity.git

    2026

  57. [57]

    Wavelength Selection for Satellite Quantum Key Distribution,

    S. Hearne, J. Horgan, N. Boujnah, D. Kilbane, S. Hearne, J. Horgan, N. Boujnah, and D. Kilbane, “Wavelength Selection for Satellite Quantum Key Distribution,”Applied Sciences, vol. 15, no. 3, Jan. 2025, company: Multidisciplinary Digital Publishing Institute Distributor: Multidisciplinary Digital Publishing Institute Institution: Multidisciplinary Digital...

    2025

  58. [58]

    Pastor-Satorras and A

    R. Pastor-Satorras and A. Vespignani,Evolution and structure of the Internet: A statistical physics ap- proach. Cambridge University Press, 2007. 4

    2007

  59. [59]

    J. Grotendorst and John von Neumann-Institut für Computing, Eds.,Quantum simulations of complex many-body systems: from theory to algorithms: winter school, 25 February - 1 March 2002, Rolduc Con- ference Centre, Kerkrade, the Netherlands ; lecture notes, ser. NIC series. Jülich: NIC-Secretariat, 2002, no. 10

    2002

  60. [60]

    Practical markov chain monte carlo,

    C. J. Geyer, “Practical markov chain monte carlo,”Statistical science, pp. 473–483, 1992

    1992

  61. [61]

    A space-suitable, high brilliant entangled photon source for satellite based quantum key distribution,

    E. Beckert, O. de Vries, R. Ursin, F.-O. Steinlechner, M. Gräfe, and M. G. Basset, “A space-suitable, high brilliant entangled photon source for satellite based quantum key distribution,” inFree-Space Laser Communications XXXI, vol. 10910. SPIE, 2019, pp. 260–273

    2019

  62. [62]

    Entanglement demonstration on board a nano-satellite,

    A. Villar, A. Lohrmann, X. Bai, T. Vergoossen, R. Bedington, C. Perumangatt, H. Y. Lim, T. Islam, A. Reezwana, Z. Tanget al., “Entanglement demonstration on board a nano-satellite,”Optica, vol. 7, no. 7, pp. 734–737, 2020

    2020

  63. [63]

    Free- space reference frame independent quantum key distribution system with photonic integrated circuit-based transmitter,

    K. Lim, M. Kim, B.-S. Choi, J. H. Baek, J.-S. Choe, K.-J. Kim, D. C. Kim, J. Oh, and C. J. Youn, “Free- space reference frame independent quantum key distribution system with photonic integrated circuit-based transmitter,”Journal of Lightwave Technology, vol. 44, no. 3, pp. 1079–1085, 2026

    2026

  64. [64]

    Critical percolation on a bethe lattice revisited,

    G. Braga, R. Sanchis, and T. Schieber, “Critical percolation on a bethe lattice revisited,”SIAM Review, vol. 47, pp. 349–365, 08 2006

    2006

  65. [65]

    Going beyond bell’s theorem,

    D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond bell’s theorem,” inBell’s theorem, quantum theory and conceptions of the universe. Springer, 1989, pp. 69–72

    1989

  66. [66]

    Three qubits can be entangled in two inequivalent ways,

    W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,”Phys. Rev. A, vol. 62, p. 062314, Nov 2000. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.62.062314

    work page doi:10.1103/physreva.62.062314 2000

  67. [67]

    Distributed measurement-based quantum computation,

    V. Danos, E. d’Hondt, P. Panangaden, and E. Kashefi, “Distributed measurement-based quantum computation,”Electronic Notes in Theoretical Computer Science, vol. 170, pp. 73–94, Jul 2007. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1571066107000564

    2007

  68. [68]

    Conference key agreement in a quantum network,

    A. Pickston, J. Ho, A. Ulibarrena, F. Grasselli, M. Proietti, C. L. Morrison, P. Barrow, F. Graffitti, and A. Fedrizzi, “Conference key agreement in a quantum network,”npj Quantum Information, vol. 9, no. 1, p. 82, 2023

    2023

  69. [69]

    Quantum secret sharing,

    M. Hillery, V. Bužek, and A. Berthiaume, “Quantum secret sharing,”Phys. Rev. A, vol. 59, pp. 1829–1834, Mar 1999. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.59.1829

    work page doi:10.1103/physreva.59.1829 1999

  70. [70]

    Degen, F

    C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantum sensing,”Reviews of Modern Physics, vol. 89, p. 035002, Jul. 2017. [Online]. Available: https://link.aps.org/doi/10.1103/RevModPhys.89.035002

    work page doi:10.1103/revmodphys.89.035002 2017

  71. [71]

    Distributed quantum sensing using continuous-variable multipartite entanglement,

    Q. Zhuang, Z. Zhang, and J. H. Shapiro, “Distributed quantum sensing using continuous-variable multipartite entanglement,”Physical Review A, vol. 97, p. 032329, Mar. 2018. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.97.032329

    work page doi:10.1103/physreva.97.032329 2018

  72. [72]

    Coffman, J

    V. Coffman, J. Kundu, and W. K. Wootters, “Distributed entanglement,”Physical Review A, vol. 61, no. 5, p. 052306, Apr. 2000. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.61.052306

    work page doi:10.1103/physreva.61.052306 2000

  73. [73]

    Distributed quantum computing: a survey,

    M. Caleffi, M. Amoretti, D. Ferrari, D. Cuomo, J. Illiano, A. Manzalini, and A. S. Cacciapuoti, “Distributed quantum computing: a survey,” 2022. [Online]. Available: https://arxiv.org/abs/2212.10609

    work page arXiv 2022

  74. [74]

    Quantum repeater for w states,

    J. Miguel-Ramiro, F. Riera-Sàbat, and W. Dür, “Quantum repeater for w states,”PRX Quantum, vol. 4, no. 4, p. 040323, 2023

    2023

  75. [75]

    Launch cost deflation and the economics of satellite deployment,

    J. Christie and P. Mitic, “Launch cost deflation and the economics of satellite deployment,”Journal Insights, vol. 1, 2022. 5

    2022

  76. [76]

    A techno-economic assessment and tradespace explo- ration of low earth orbit mega-constellations,

    K. T. Li, C. A. Hofmann, H. Reder, and A. Knopp, “A techno-economic assessment and tradespace explo- ration of low earth orbit mega-constellations,”IEEE Communications Magazine, vol. 61, no. 2, pp. 24–30, 2022

    2022

  77. [77]

    Modern small satellites-changing the economics of space,

    M. N. Sweeting, “Modern small satellites-changing the economics of space,”Proceedings of the IEEE, vol. 106, no. 3, pp. 343–361, 2018. 6

    2018