Operational limits to entanglement-based satellite quantum key distribution

TL;DR

Addresses the problem of evaluating entanglement-based SatQKD performance under finite-key constraints for a dual-downlink BBM92 configuration. Approach: an end-to-end high-fidelity model of orbital dynamics, link losses, background noise, and detector effects integrated with a finite-key security analysis for BBM92, including threshold-based block construction and a brute-force optimization of the finite-key length $\ell/m$ under a composable security bound $\epsilon_{QKD}$. Findings: optimized SKL is achievable across realistic overpass geometries; at a baseline of 500 km altitude and 500 km ground-station separation, the annual SKL is on the order of $\text{SKL}_{\text{year}} \approx 870~\text{Mb}$, with daylight operation feasible given background mitigation; very low Earth orbits can improve keys for long baselines. Significance: provides quantitative design guidelines for near-term SatQKD missions and enables co-design of satellite constellations and ground infrastructure for global entanglement distribution, and offers a framework extendable to multi-OGS and repeater-enabled networks.

Abstract

Space-based distribution of quantum entanglement will be essential for global quantum networking and secure communications. Modelling and analysis of the performance of satellite entanglement pair distribution is important for the architecture and design of constellations and space systems. 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. Therefore, there is a need for a comprehensive study of finite-key effects in the context of direct dual downlink quantum key distribution taking into account the characteristics of the overpass geometries. 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. We integrate this with a rigorous finite-key security framework for the BBM92 protocol to optimise secret key length across different overpass geometries, orbital altitudes, and optical ground station (OGS) separations. These results provide quantitative performance bounds and design guidelines for near-term SatQKD missions, enabling informed trade-offs between satellite payload complexity, ground infrastructure, and achievable secure key throughput.

Figures (9)

• Figure 1: Dual downlink satellite overpass geometry. Depiction of a satellite geometry for an asymmetrical overpass at the $t_0$ point. The orbit can be described through the relation between the satellite's ground track and the OGS baseline, or more specifically the angular rotation $\Phi$ and the distance offset, $\Delta$ from the baseline midpoint. The OGSs shown are located equidistant from the North Pole marked by a black dot.
• Figure 2: Link model for satellite-to-ground QKD. (top) Instantaneous link efficiency for satellite overpasses within the visible region with $\Delta=0$ and varying $\Phi$, with $\lambda=785$ nm and OGS separation of $d = 2000$ km. The white region illustrates where either satellite falls below $\theta_\text{min}=10^\circ$. Note that the smallest transmission time corresponds to the satellite passing directly overhead both OGSs, where the ground track traces the great circle arc between the OGSs. Further, the two loss minima is due to postselecting on coincident counts and emerges at large $d$. (bottom) Combined loss vs overpass time for different $\Phi$, illustrating a minimum loss of 56 dB for a zenith overpass ($\theta^i_\text{max} = 90^\circ$) for $i \in \{A, B\}$. All other system parameters in Table \ref{['tab:system_parameters']}.
• Figure 3: Performance with block size and background illumination. Finite key length, $\ell$, as a function of block size for increasing background photon levels, parameterised by a scaling factor $f$ relative to a baseline background detection probability ${p_\text{bg}=10^{-7}}$. Curves correspond to night-time and twilight (twil.) operating conditions, with darker solid colours indicating lower background levels and progressively lighter dashed colours representing increasing ambient illumination. Shaded regions highlight the night-time and twilight regimes. All data shown corresponds to a zenith-zenith overpass, with $h = 500$ km and $d = 500$ km.
• Figure 4: Finite SKL with different system configurations. We consider key generation from a single zenith-zenith overpass $\{\Phi=0^\circ,\Delta=0$ m}. (a) finite-key BBM92 performance with different satellite altitudes, $h$. The grey region indicated very LEO and the red shaded region LEO orbits. The vertical black line marks the altitude of the international space station and the red dashed line of the Micius satellite. (b) illustrates the key performance with OGS separation distances, $d$. The crossover in the key generation performance for different satellite altitudes quantifies the trade-off between the maximum viewing distance on Earth and operating losses. The vertical dashed line indicates the nominal altitude of 500 km with the mark indicating the simulated key length achieved using a subset of parameters aligned to the Micius satellite. Both plots consider a zenith-zenith overpass. System parameters as in Table \ref{['tab:system_parameters']}.
• Figure 5: Finite SKL for different overpass geometries. We assume $d=500\ km$ and $h=500\ km$. a) SKL evaluated over the full overpass geometry parameter space, defined by the angular offset $\Phi$ and distance offset, $\Delta$, of the satellite ground-track intersection relative to the OGS baseline. Each longitudinal coordinate, $\gamma$, maps to a unique point $(\Delta(\gamma), \Phi(\gamma))$ in this parameter space, tracing a trajectory over the course of a year. The red line at $\Delta=0$, for which $\Phi(\gamma) = \gamma$, reflects our baseline system configuration. The corresponding SKL along this trajectory is illustrated in b). As the Earth rotates, $\gamma$ is uniformly sampled. The secret key yield per pass decreases with increasing off-axis angles. The area under the curve informs the annual SKL via Eq. \ref{['eqn:annual_SKL_long']}. System parameters are given in Table \ref{['tab:system_parameters']}.