Relativistic Effects and Retardation in Continuous Variable Quantum Key Distribution Significantly Impact Frequency Shifts

The increasing demand for secure communication drives exploration of quantum key distribution (QKD) via satellite, but accurately modelling signal behaviour in space presents significant challenges. Emanuel Schlake, Jan P. Hackstein, and Roy Barzel, alongside colleagues at ZARM, University of Bremen, investigate how relativistic effects and signal delays impact the performance of continuous variable QKD systems. Their work systematically separates and quantifies frequency shifts arising from satellite motion and the finite speed of light, revealing that both relativistic corrections and signal delays contribute significantly to communication errors. This detailed analysis demonstrates that neglecting these effects can substantially reduce secure key rates, and highlights the necessity of incorporating them into future designs for space-based quantum communication networks.

Relativistic Shifts Impact Quantum Key Distribution

Space-based quantum communication relies on satellites and ground stations exchanging optical signals, which experience frequency shifts due to relativistic effects and the finite speed of light. This research investigates these frequency shifts and their impact on continuous variable quantum key distribution (CVQKD), analysing how they affect protocol performance considering both special and general relativistic contributions. The team developed a comprehensive model to predict signal degradation and optimise system parameters, enabling countermeasures to ensure secure quantum communication links between space- and ground-based stations. The findings demonstrate the feasibility of implementing CVQKD in space, provided appropriate compensation strategies address the observed frequency shifts.

The research systematically separates the frequency shift into contributions from longitudinal Doppler effects, relativistic corrections, and corrections due to signal propagation delay, or retardation. Analyses reveal that relativistic corrections to satellite orbits are negligible compared to gravitational and special relativistic time dilation, while the retardation effect is surprisingly comparable in magnitude to relativistic contributions, highlighting its importance in precise frequency measurements. Investigations assess the significance of these effects by modelling the impact on CVQKD systems.

Relativistic Redshift Impacts Satellite Communication Accuracy

This research examines the accuracy of approximations used to calculate redshift in satellite communication, particularly when dealing with relativistic effects and the curvature of spacetime. The study focuses on when simplified models are valid and when they break down, considering factors such as light bending around the Earth and the precession of a satellite’s orbit. Simulations cover a variety of orbit constellations, including geostationary, medium Earth orbit, highly eccentric, and low Earth orbits, with a particular emphasis on the implications for quantum key distribution (QKD), where even small errors can compromise security.

The research demonstrates that light bending can cause significant errors in redshift calculations, especially when signals pass close to the Earth’s centre. The periapsis shift accumulates errors over time, largest at the point of closest approach in the orbit. Approximations used to calculate redshift are valid only for limited periods, particularly for highly eccentric orbits or signals passing close to Earth. Highly eccentric orbits are especially sensitive to errors in redshift calculations due to large variations in satellite velocity. The deviation between true and approximated redshift can reach the magnitude of relativistic effects, indicating a breakdown in the approximations.

The findings highlight the importance of careful consideration of satellite constellations when designing communication systems, especially for QKD. The limitations of approximations must be understood, and more accurate models may be needed for high-precision applications. For long-term communication, the cumulative effect of the periapsis shift must be accounted for, and a trade-off exists between accuracy and computational cost.

Frequency Shift Analysis for Space Communication

This research systematically analyses the frequency shift experienced in space-based optical communication, considering both relativistic effects and the impact of signal propagation delay, or retardation. The team demonstrates that while leading-order relativistic contributions depend on orbital radius and speed, the retardation effect is of comparable magnitude and must be accounted for in accurate communication modelling. Investigations reveal that the retardation effect is particularly significant in downlink configurations and inter-satellite links, where relative velocities are higher.

Scientists modelled the impact of these frequency shifts on continuous-variable quantum key distribution (CVQKD), treating the resulting mode mismatch as a lossy quantum channel. This analysis demonstrates that both relativistic effects and retardation significantly influence communication performance and should be incorporated into system designs. The team acknowledges that for orbits with very large semi-major axes and eccentricities, higher-order effects may become relevant, and suggests utilising numerical tools for more detailed analysis in such cases.