Global-scale quantum networking using hybrid-channel quantum repeaters with relays based on a chain of balloons

Abstract

Global-scale entanglement distribution has been a formidable challenge due to the unavoidable losses in communication channels. Here, we propose a novel backbone channel for quantum network based on balloon-based aerial relays. We demonstrate for the first time that the atmospheric disturbances in balloon-based channels can be almost eliminated through optimizing beam waist positions and employing a series of adaptive optics systems, which boosts the channel efficiency to -21 dB over a 10,000 km distance, outperforming satellite-based relays by 12 dB with same device parameters. We then propose a global-scale quantum networking scheme based on hybrid-channel quantum repeaters that combine ground-based quantum repeaters and balloon-based aerial relays. Servers are interconnected globally via a chain of balloons, while clients link to local servers through fiber connections, facilitating rapid client switching and network scalability. Our simulations, employing state-of-the-art Eu$^{3+}$:Y$_2$SiO$_5$ quantum memories and mature entanglement sources based on spontaneous parametric down-conversion, demonstrate an entanglement distribution rate in the sub-Hertz range between clients separated by 10,000 km. This approach offers a practical path toward global quantum networking in the near future.

Figures (12)

• Figure 1: Channel efficiency of balloon-based relays as a function of the distance between servers, based on parameters listed in Appendix Table \ref{['tab:simulation_parameters']}. (a) Optimized channel efficiency of balloon-based relays. Solid colored curves represent different relay balloon counts, showing that longer distances require more relay balloons (optimally spaced at $\sim$110 km). The black dashed line shows the maximum efficiency across all possible relay numbers, while the green dashed line shows the maximum efficiency achievable with satellite-based relays for comparison. We note that our simulation for satellite-based relays is more rigorous than that reported in Ref. goswami_satellite-relayed_2023, by further including wavefront distortion in both uplink and downlink channels (Appendix Section \ref{['Satellite']}). (b) Comparison of maximum channel efficiency of balloon-based relays under different configurations. Optimized waist: Beam waist position optimized with (black dashed) and without (black solid) AO. Mid-path waist: Beam waist fixed at the midpoint of the path without AO (orange solid). Tx waist: Beam waist fixed at transmitter without AO (blue solid). At 10,000 km, our optimized configuration provides a 55 dB improvement over the typical mid-path waist configuration, establishing balloon-based relays as a practical backbone solution for global-scale quantum networking.
• Figure 2: The hybrid quadruple-link quantum repeater (H4QR) for global-scale entanglement distribution, with aerial relays and ground-based quantum repeaters. (a) Schematic representation of the connections between global-scale separated clients (Alice and Bob). Entanglement distribution between Alice and Bob involves four connections: two metropolitan fiber links (Alice $\leftrightarrow$ Charlie and Bob $\leftrightarrow$ David) and two balloon-based free-space relays (Charlie $\leftrightarrow$ Elbert and David $\leftrightarrow$ Elbert). Inset: One server serves multiple nearby clients via fiber links. These Clients can operate in sequence with fast optical switches or in parallel through wavelength multiplexing. (b) Detailed implementation of H4QR. Elementary entanglement is generated using Bell-state measurements (BSM1, BSM3, BSM5, BSM7) on photons from entangled photon pair sources (EPPSs). Quantum memories QM2 and QM5 temporarily store entangled photons until they are retrieved for synchronized entanglement swapping via BSM2 and BSM6. The final BSM4, performed on photons retrieved from QM3 and QM4, heralds the end-to-end entanglement between QM1 and QM6, completing the distribution process.
• Figure 3: Theoretical and simulated entanglement distribution time of H4QR. The blue and red line represent the theoretical upper bound and the lower bound, respectively. The orange circles denote the numerical simulation based on Monte Carlo method. For short distances, the lower bound fits well with the simulation. For long distances, the simulated results getting closer to the upper bound.
• Figure 4: Theoretical upper bound of EDR as a function of the mode capacity of QMs at a distribution distance of $3000$ km. The blue dashed line: the horizontal axis represents the number of modes $m$, with $n=1$ fixed. The red solid line: the horizontal axis represents the number of modes $n$, with $m=1$ fixed.
• Figure 5: Representation of the geometrical parameters used in our simulation. Balloons are positioned at an altitude $H$, and ground station transmitters are located at an altitude $h_0$. (a) In the uplink and downlink channels, $L_v$ is the light propagation distance (Eq.\ref{['eq.L_v']}). $\theta_z$ is the zenith angle, which is set to zero in our simulation as the balloons are assumed to float directly above the observatories of servers. (b) In the horizontal channel, $L_h$ is the light propagation distance (Eq.\ref{['eq.L_h']}), $R_E$ is the radius of the Earth, $z_0$ is the arc length between two ground stations, $\theta_E$ is the corresponding subtending angle (Eq.\ref{['eq.thetaE']}), $h_\text{min}$ is the minimum height along the path between the two balloons (Eq.\ref{['eq.hmin']}). For all relay balloons, light is not coupled into single-mode fibers (SMFs) but corrected by AO systems to reduce channel loss.