Space-based quantum communication naturally involves satellites and ground stations exchanging optical signals at high altitudes and large relative velocities. Starting from general relativistic considerations, we systematically separate the frequency shift into longitudinal Doppler contributions, relativistic corrections, and corrections from the propagation delay (retardation). We find the relativistic corrections to the Keplerian satellite orbits to be negligible on the considered timescale, compared to the gravitational and special relativistic time dilation contributions to the frequency shift. Somewhat surprisingly, we find the contribution from the retardation effect to be on the same order of magnitude as the relativistic contributions. To analyze the significance of these effects, we investigate secret key capacities for a continuous variable quantum key distribution protocol for various configurations of satellite orbits and ground stations. We find that the corrections from relativistic effects and retardation significantly impact the communication performance and should be taken into account.
Space-based quantum communication naturally involves satellites and ground stations exchanging optical signals at high altitudes and large relative velocities. Starting from general relativistic considerations, we systematically separate the frequency shift into longitudinal Doppler contributions, relativistic corrections, and corrections from the propagation delay (retardation). We find the relativistic corrections to the Keplerian satellite orbits to be negligible on the considered timescale, compared to the gravitational and special relativistic time dilation contributions to the frequency shift. Somewhat surprisingly, we find the contribution from the retardation effect to be on the same order of magnitude as the relativistic contributions. To analyze the significance of these effects, we investigate secret key capacities for a continuous variable quantum key distribution protocol for various configurations of satellite orbits and ground stations. We find that the corrections from relativistic effects and retardation significantly impact the communication performance and should be taken into account.
Abstract High relative velocities and large distances in space-based quantum communication with satellites in lower earth orbits can lead to significant Doppler shifts and delays of the signal impairing the achievable performance if uncorrected. We analyze the influence of systematic and stochastic Doppler shift and delay in the specific case of a continuous variable quantum key distribution (CV-QKD) protocol and identify the generalized correlation function, the ambiguity function, as a decisive measure of performance loss. Investigating the generalized correlations as well as private capacity bounds for specific choices of spectral amplitude shape (Gaussian, single- and double-sided Lorentzian), we find that this choice has a significant impact on the robustness of the quantum communication protocol to spectral and temporal synchronization errors. We conclude that optimizing the pulse shape can be a building block in the resilient design of quantum network infrastructure.
Abstract Quantum key distribution (QKD) is a method for securely exchanging keys based on quantum mechanics. QKD has been thoroughly examined for terrestrial and near-Earth satellite applications; however, forthcoming deep-space links are anticipated to experience considerable relativistic effects. Quantum states can be altered in these circumstances by relative motion between terminals and by gravitational effects, which may affect entan-glement, measurement outcomes, and overall security. The effectiveness of entanglement-based quantum key distribution (QKD) in relativistic motion is investigated in this work, with particular attention to deep-space optical communication. The quantum channel model includes Wigner rotations due to Lorentz transformations, polarization mixing due to Doppler shift, and redshift due to gravity. This method gives us new ways to analyze the quantum bit error rate (QBER), quantum entanglement fidelity, Bell inequality violation , and secret key rate. Our numerical simulations show that when the relative velocity becomes high enough, the polarization correlations start to break down significantly. This leads to more errors in the quantum bits, making it harder to generate a secure secret key. Even though quantum nonlocality persists at these speeds, relativistic effects make it much harder to actually extract a secure key.
Australia and New Zealand are currently developing an optical communications ground station network to test technologies for optical and quantum communications that will enable faster data transfers and security during information exchange. A goal of the network is to implement Gaussian modulated continuous variable quantum key distribution (GM-CVQKD) between LEO satellites and optical ground stations. This protocol offers quantum cryptography, providing information-theoretic security through quantum mechanics and is compatible with hardware needed for coherent optical communications that satellites are starting to use to combat the crowded spectrum from increased traffic in radio-frequency communications. GM-CVQKD avoids the need for the specialised and complex equipment required by discrete variable QKD to achieve secret key exchange, as it can use cost-effective commercially available off-the-shelf hardware. We present a study to determine the feasibility of a proposed implementation of GM-CVQKD. As a first step, a model of the quantum signal downlink propagation from a LEO satellite to an optical ground station (OGS) has been created. This was used to explore adverse effects from varying atmospheric conditions, the Doppler shift owing to the relative motion between a LEO satellite and an OGS, and the presence of an attack/hack from an eavesdropper. The results show that suitable atmospheric conditions (negligible turbulence and higher visibility) produce a larger positive secret key rate (SKR) while less favourable conditions (high turbulence and lower visibility) significantly decrease the achievable SKRs. The effects of Doppler shift are negligible and still permit a positive SKR. The protocol allows the presence of an eavesdropper to be detected so that communications can be terminated. The results indicate that GM-CVQKD is a viable protocol for space-based QKD and is a stepping-stone towards a global quantum network.
Abstract: Terrestrial fiber-optic quantum networks are subject to exponential photon attenuation (≈ 0.2 dB/km at 1550 nm), constraining unrepeatered ground quantum key distribution (QKD) and entanglement distribution to distances below a few hundred kilometers. While quantum repeaters remain technologically nascent, intercontinental sovereign security mandates unhackable, physical-layer cryptographic connectivity across transoceanic baselines. Satellite-based quantum communications operating in Low Earth Orbit (LEO, altitude h ≈ 500–800 km) provide a transformative solution by exploiting near-vacuum propagation for the vast majority of the optical path, bypassing terrestrial exponential loss. However, high-velocity LEO satellite platforms (v ≈ 7.6 km/s) introduce severe relativistic and atmospheric distortions that rapidly destroy quantum coherence: (1) kinematic Doppler shifts (Δν/ν ≈ ± 2.5 × 10^-5) and general relativistic gravitational redshifts alter photon wavepackets and relative phase trajectories; (2) dynamic spacetime curvature induces Wigner phase rotations on polarization-entangled states; and (3) atmospheric turbulence creates beam wandering, wavefront aberration, and photon arrival time jitter across the troposphere (0–15 km). This monograph establishes the theoretical framework, mathematical formulation, and solid-state engineering architecture for the PHOENIX_ORBIT space-to-ground quantum communications network. We derive: (1) an exact relativistic transformation matrix incorporating Kerr-Schwarzschild spacetime metric perturbations and orbital kinematics, coupled to an ultra-fast electro-optic dynamic phase compensator operating with sub-picosecond latency; (2) an adaptive optics (AO) closed-loop architecture combining high-bandwidth tip-tilt mirrors and deformable piezo-actuators calibrated to the local Fried parameter r_0 and Greenwood frequency f_G; (3) an entanglement routing protocol linking space-borne spontaneous parametric down-conversion (SPDC) sources to ground-based PHOENIX_ROUTER quantum data centers; and (4) an asymptotic security proof verifying Clauser-Horne-Shimony-Holt (CHSH) Bell inequality violation (S ≥ 2√2 − ε) under non-inertial reference frame drift. Our architecture achieves a continuous secret key rate exceeding 1.2 Mbps per satellite pass with a quantum bit error rate QBER < 1.4%, providing an unassailable physical-layer foundation for global sovereign data sovereignty.
Establishing information-theoretically secure communication between arbitrary locations on Earth is a central goal of quantum networking, for which space-based distribution of quantum entanglement is a leading approach. Modelling and analysis of the performance of satellite entanglement pair distribution is therefore important for the architecture and design of future constellations and space systems. However, 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. Quantifying these effects under realistic orbital conditions is therefore essential for the design of practical satellite quantum communication systems. Here, 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. Integrating this with a finite-key security framework for the BBM92 protocol, we optimise the secret key length across different overpass geometries, orbital altitudes, and optical ground station (OGS) separations. We show that secure key generation remains feasible in early clear daytime conditions using baseline parameters representative of current technologies, while showing that modest system improvements could further extend daytime operation. Finally, we evaluate the annual secret key performance for representative intercity-scale OGS pairings. Our results provide quantitative performance bounds and practical design guidelines for near-term entanglement-based satellite QKD, enabling informed trade-offs between satellite payload complexity, ground infrastructure, and achievable secure key throughput.
Abstract Future quantum communication infrastructures will rely on both terrestrial and space-based links integrating high-performance optical systems engineered for this purpose. In space-based downlinks in particular, the loss budget and the variations in the signal propagation due to atmospheric turbulence effects impose a careful optimization of the coupling of light in single-mode fibers required for interfacing with the receiving stations and the ground networks. In this work, we perform a comprehensive study of the role of adaptive optics (AO) in this optimization, focusing on realistic baseline configurations of prepare-and-measure quantum key distribution, with both discrete and continuous-variable encoding, and including finite-size effects. Our analysis uses existing experimental turbulence datasets at both day and night time to model the coupled signal statistics following a wavefront distortion correction with AO, and allows us to estimate the secret key rate for a range of critical parameters, such as turbulence strength, satellite altitude and ground telescope diameter. The results we derive illustrate the interest of adopting advanced AO techniques in several practical configurations.