Satellite Quantum Key Distribution

• Satellite-based QKD is a secure communication method that uses low-loss free-space links between satellites and ground stations to exchange quantum keys over global distances.
• It employs both single-downlink (trusted-node) and dual-downlink (entanglement distribution) architectures to balance high key rates with reduced trust requirements.
• Optimized scheduling and weather-aware filtering are essential for maintaining high throughput and fairness in dynamic satellite QKD networks.

Satellite-based quantum key distribution (QKD) is an advanced scheme for secure key sharing over global distances, leveraging the low attenuation of free-space optical links between satellites and terrestrial ground stations. Unlike terrestrial fiber-based QKD, which is constrained by exponential loss limiting span to several hundred kilometers, satellite-based systems exploit quadratic free-space loss and LEO (Low-Earth Orbit) availability to provide high-rate, long-distance quantum-secure communications. Satellite QKD has evolved to encompass various architectures, protocols, hardware platforms, and large-scale scheduling optimizations suitable for both point-to-point and networked deployment (Orsucci et al., 8 Apr 2024, Hossain et al., 14 Dec 2025).

1. System and Channel Model

Satellite QKD operates predominantly in two network architectures: the single-downlink (trusted node) and the dual-downlink (entanglement distribution). In the single-downlink scenario, each satellite establishes a BB84 QKD link separately with each ground station, generating key pools $K_{s,g}$, which subsequently enable key sharing across any ground station pair via the satellite acting as a trusted relay. The channel is modeled as a sequence of time slots $t$, where satellite $s$ and ground station $g$ are characterized by slant distance $D_{s,g}(t)$, elevation $\theta_{s,g}(t)$, and time-varying optical transmissivity:

$$\eta_{s,g}(t) = \eta_{\rm opt} \cdot \left( \frac{\pi w_0}{\lambda D_{s,g}(t)} \right)^2 \cdot \eta_{\rm atm}(\alpha_g(t), \theta_{s,g}(t)).$$

Atmospheric attenuation $\eta_{\rm atm}$ is locally and temporally dependent, incorporating MODTRAN-derived coefficients and incorporating cloud coverage $c_{t,g}$ as a multiplicative loss term. Instantaneous key rates,

$$R_{s,g}(t) = (1-c_{t,g}) \, \nu \, [\mu\,\eta_{s,g}(t)p_d + Y_0]\,[1-2h(E_{s,g}(t))],$$

depend on pulse rate $\nu$, mean photon number $\mu$, detector efficiency $p_d$, background click probability $Y_0$, and the observed quantum bit error rate (QBER) $E_{s,g}(t)$. The QBER incorporates both system errors and background/ambient noise.

2. Scheduling and Network Optimization

Satellite-based QKD systems involving large constellations and globally distributed ground stations require coordinated scheduling algorithms to maximize network-wide performance metrics such as total throughput and fairness across ground station pairs. The scheduling landscape encompasses:

• Visibility constraints: Ensure that only satellite-ground pairs with elevation above a given threshold ($\theta_{min}$) are considered.
• Mutual exclusivity constraints: Each satellite or ground station is engaged in at most one QKD link per slot.
• Key pool assignment: Accumulation of link-wise secret bits $K_{s,g}$ across time slots, followed by allocation to user pairs via the trusted node relay protocol.

Optimization objectives include total throughput (maximizing $R_{total} = \sum_{(g_a, g_b)} R_{g_a, g_b}$) and max-min fairness (maximizing $R_{min} = \min_{(g_a,g_b)} R_{g_a,g_b}$), formulated as coupled mixed-integer programs across $O(T |S| |G|)$ variables.

The "opportunistic scheduling" approach uses a two-phase procedure: (1) fast, distributed allocation of link resources via bipartite matching with dynamic Lagrange multipliers, and (2) integer programming to allocate key pools from satellites to ground-station pairs to satisfy fairness and capacity constraints (Hossain et al., 14 Dec 2025).

3. Performance, Weather, and Operational Tradeoffs

Simulation on realistic constellations (e.g., 400 LEO satellites; up to 11 continental ground sites) shows the following:

• Throughput and fairness: Opportunistic algorithms (e.g., Op-RR) attain 72–76% of theoretical maximum throughput and at least 95% of max-min fairness, while simple heuristics (round-robin, greedy) fall below 50% for either objective.
• Cloud coverage/meteorology: Without filtering, adverse weather can severely degrade key rates and fairness. Simple link pre-filtering (disregarding links with $c_{t,g} > 0.8$) restores throughput by up to $2.9\times$ and fairness by up to $1.8\times$.
• Regional vs. global: Max-Sum optimization for regional ground-station clusters sacrifices fairness for total key volume. Opportunistic policies balance both metrics (maintaining $>90\%$ of each).
• Computational efficiency: Exact MIP formulations consume $>100$ GB RAM and hours of runtime; the opportunistic routines scale to global networks within minutes.

The chosen scheduling routine determines network behavior under seasonality and cloud variation. June's typically clear conditions yield the highest throughput; filtering and scheduling adapt dynamically to maximize performance in winter or monsoon periods.

4. Architectural Implications: Single- vs Dual-Downlink

• Single-downlink (trusted-node): Facilitates QKD between arbitrary ground station pairs without simultaneous visibility. Achieves higher key rates (since only one free-space link is traversed per key exchange) and expanded global connectivity, at the cost of requiring trust in the satellite’s key storage/relay. Useful for multi-hop global key sharing where security requirements can be balanced against operational utility.
• Dual-downlink (entanglement): Satellite distributes pairs of entangled photons simultaneously to two ground stations. Offers device-independent security but is restricted in geometric reach (only pairs with coincident satellite visibility can be linked) and suffers quadratic decrease in rate due to double-transmission loss.

The tradeoff is clear: single-downlink is operationally preferable for high-throughput and arbitrary-pair connectivity, while dual-downlink strictly prioritizes trust minimization at the expense of flexibility and rate (Hossain et al., 14 Dec 2025).

5. Key Rate Formulas and Security Considerations

Secret key rate per time slot is derived under BB84 with decoy states, accounting for time-varying loss, QBER, and finite statistics. Asymptotically,

$r_{s,g}(t) = 1 - 2h(E_{s,g}(t)),$

with the per-slot secret bit output modulated by instantaneous transmissivity and error estimation. Resource constraints (detector deadtime, classical bandwidth) and composable security thresholds require real-time adaptation of QKD protocol parameters in line with current channel state. Security for trusted-node architectures pivots on the satellite being uncompromised during key relaying, although parallel trusted-node protocols can mitigate trust centralization (Santis et al., 12 Jun 2024).

6. Scheduling Algorithmic Structure and Scalability

The practical scheduler proceeds in two explicit phases:

1. Link-wise resource allocation: Dynamic per-link Lagrange multipliers prioritize under-served satellite–ground links. In each slot, a bipartite max-weight matching selects the link set to activate, optimizing weighted instantaneous key rates. Multipliers are updated via subgradient steps to penalize under-provisioned links.
2. Key pool to pairwise user allocation: With key pools accumulated, small integer programs reassign key material to user pairs to maximize fairness and/or total key distribution.

The algorithm naturally exploits time-variable link conditions (transiently high transmissivity, cloud-free intervals), resulting in robust network performance across seasons and weather regimes. Computation times are orders of magnitude lower than full MIP solutions, enabling real-time or large-scale network orchestration.

7. Practical Insights and Future Directions

Operationally, satellite QKD networks benefit from:

• Dynamic weather-aware scheduling and filtering, maximizing use of viable links.
• Opportunistic policies that balance total key volume with per-pair fairness, even in networks with hundreds of satellites and ground stations.
• Flexible architectural choices (e.g., trusted-node enabling global coverage vs dual-downlink for maximal trust-minimization).
• Real-time adaptation to satellite–ground channel variability, leveraging link-state estimation and rapid scheduling.
• Integration of improved trusted node and parallel trusted node architectures for enhanced resilience and distributed trust (Santis et al., 12 Jun 2024).

Future work will focus on even more fine-grained weather integration, scaling to variable-orbit mega-constellations, and integration with terrestrial QKD networks for global quantum-secure communication (Hossain et al., 14 Dec 2025).