Exploiting Spatial Diversity in Earth-to-Satellite Quantum-Classical Communications

Despite being an integral part of the vision of quantum Internet, Earth-to-satellite (uplink) quantum communications have been considered more challenging than their satellite-to-Earth (downlink) counterparts due to the severe channel-loss fluctuations (fading) induced by atmospheric turbulence. The question of how to address the negative impact of fading on Earth-to-satellite quantum communications remains largely an open issue. In this work, we explore the feasibility of exploiting spatial diversity as a means of fading mitigation in Earth-to-satellite Continuous-Variable (CV) quantum-classical optical communications. We demonstrate, via both our theoretical analyses of quantum-state evolution and our detailed numerical simulations of uplink optical channels, that the use of spatial diversity can improve the effectiveness of entanglement distribution through the use of multiple transmitting ground stations and a single satellite with multiple receiving apertures. We further show that the transfer of both large (classically-encoded) and small (quantum-modulated) coherent states can benefit from the use of diversity over fading channels. Our work represents the first quantitative investigation into the use of spatial diversity for satellite-based quantum communications in the uplink direction, showing under what circumstances this fading-mitigation paradigm, which has been widely adopted in classical communications, can be helpful within the context of Earth-to-satellite CV quantum communications.

💡 Research Summary

The paper tackles the long‑standing challenge of Earth‑to‑satellite (uplink) quantum communication, where atmospheric turbulence induces severe fading that dramatically reduces the reliability of continuous‑variable (CV) quantum protocols. While most satellite‑based quantum experiments have relied on downlink channels because the beam is already broadened when it encounters turbulence, the authors argue that uplink configurations are essential for flexible ground‑based quantum sources, easier upgrades, and enhanced security against attacks on the satellite receiver.

To mitigate uplink fading, the authors propose a spatial‑diversity architecture in which M geographically separated ground stations simultaneously transmit portions of the same quantum signal to a Low‑Earth‑Orbit (LEO) satellite equipped with M independent receiving apertures. Each ground station receives an equal share of the original state via a network of beam splitters, and the satellite coherently combines the M incoming beams using an optical combining module (multiple beam splitters with phase alignment). The key assumptions are: (i) the sub‑channels are statistically independent because the transmitters are spaced far beyond the atmospheric coherence length (centimetres), (ii) the quantum state distribution among the ground stations is loss‑free, and (iii) the satellite’s pointing and tracking errors are negligible compared to turbulence‑induced beam wander.

Channel modelling follows standard atmospheric optics: the transmissivity T_j of each sub‑channel is treated as an independent random variable with a probability density derived from log‑normal or gamma‑gamma turbulence statistics. Excess noise at the receiver is taken as ε_j = ε_A · T_j with ε_A = 0.03 shot‑noise units (SNU). The authors first analyse entanglement distribution by sending a two‑mode squeezed Gaussian state through the diversified uplink. Using the logarithmic negativity as a lower bound, they show that the effective average transmissivity ⟨T⟩ improves with the diversity order M, thereby raising the entanglement‑preservation threshold. Numerical results indicate that moving from M = 1 to M = 4 can increase the entanglement lower bound by roughly 2 dB under the same mean loss, allowing CV‑QKD to operate at significantly higher loss levels than a single‑channel link.

The second major contribution concerns Simultaneous Quantum‑Classical Communication (SQCC). In this scheme a large classical coherent state carries the bulk of the information while a small quantum modulation encodes the secret key or quantum data. The authors apply maximal‑likelihood (or equal‑gain) combining across the M sub‑channels, which averages out the fading‑induced fluctuations in signal‑to‑noise ratio (SNR). Simulations reveal that for M ≥ 3 the classical bit‑error rate (BER) drops below 10⁻⁶ and the secret‑key rate of a CV‑QKD protocol recovers to ≈0.5 bit per pulse, even when the average channel loss exceeds 20 dB.

Implementation considerations are discussed in detail. Accurate time synchronization (to compensate for differing propagation delays among the sub‑channels) is required; the authors cite the sub‑nanosecond synchronization achieved in recent uplink quantum teleportation experiments. High‑precision pointing and tracking (error < 3 µrad) are assumed achievable with current technology, and the impact of beam overlap at the satellite is deliberately suppressed by careful optical design, representing a worst‑case scenario for diversity gain.

The simulation framework incorporates realistic parameters: LEO altitude ≈ 500 km, refractive‑index structure constant C_n² ≈ 10⁻¹⁴ m⁻²⁄³, ground transmitter aperture 10 cm, satellite receiver aperture 20 cm, and a turbulence‑induced beam‑wander variance derived from standard models. Results consistently show that increasing the diversity order yields a super‑linear improvement in both entanglement distribution and SQCC performance, confirming that spatial diversity is a viable and powerful tool for uplink quantum communications.

In conclusion, this work provides the first quantitative evidence that spatial diversity—long a staple of classical free‑space optical links—can be harnessed to overcome atmospheric fading in Earth‑to‑satellite CV quantum‑classical communication. The findings pave the way for practical uplink quantum networks, offering flexibility in ground‑based source deployment, resilience against deep fades, and enhanced security, all of which are essential for the realization of a global quantum internet.