A Theoretical Framework for an Earth-to-Moon Quantum Uplink Architecture (revised)A link-budget framework for a direct decoy-state BB84 uplink at 1550 nm from Hanle, Ladakh, to a 0.5 m lunar receiver, with adaptive optics, a core–halo beam model and log-normal fading. At night the link gives about 90 bit/s of secure key (80–101 bit/s over the lunar distance range), averaging about 1.3 Mbit per day.This revision corrects the point-ahead angle, models the Earth-shine background seen by the lunar receiver (daytime operation is ruled out), adds finite-key effects, and removes overstated security claims. Includes the verification script.
A Theoretical Framework for an Earth-to-Moon Quantum Uplink Architecture (revised)A link-budget framework for a direct decoy-state BB84 uplink at 1550 nm from Hanle, Ladakh, to a 0.5 m lunar receiver, with adaptive optics, a core–halo beam model and log-normal fading. At night the link gives about 90 bit/s of secure key (80–101 bit/s over the lunar distance range), averaging about 1.3 Mbit per day.This revision corrects the point-ahead angle, models the Earth-shine background seen by the lunar receiver (daytime operation is ruled out), adds finite-key effects, and removes overstated security claims. Includes the verification script.
A Mathematical Framework for a Lunar-to-Mars Quantum Key Distribution Architecture (revised)A link-budget framework for a direct, single-hop entanglement-based (BBM92) QKD link at 1550 nm from a lunar terminal to a Martian receiver, using 10 m apertures on a 30–40 year technology horizon. The link gives about 6 bit/s of secure key at the mean distance and about 115 bit/s near opposition. Key generation stops when the Martian dust optical depth exceeds about 2.8, and the link is unavailable for roughly two to three months around each solar conjunction.This revision derives the QBER from a single noise model, models dust by optical depth, adds the solar-conjunction outage, and corrects the relativistic clock drift to include solar gravity (433 µs/day). Includes the verification script.
Satellite-based free-space quantum key distribution (QKD) provides a practical framework for achieving secure global communication beyond the limitations of optical fibers. In this work, the quantum bit error rate (QBER) and secure key rate of four representative protocols-BB84, B92, BBM92, and E91 are investigated over low earth orbit (LEO) links in both uplink and downlink configurations. The optical link is modeled using a Gaussian beam formalism, incorporating the effects of diffraction, pointing errors, atmospheric turbulence, and background noise contributions. The protocols are examined under day and night-time operating conditions, and their dependence on the zenith angle is analyzed. The findings show that downlink links generally exhibit lower QBER and higher secure key rates than uplinks, and among prepare-and-measure schemes, BB84 consistently outperforms B92, while in entanglement-based approaches, BBM92 achieves higher key rates than E91.
Received optical power determines photon arrival flux, but photon arrival flux does not certify a quantum key. This paper gives a deployment-independent interface from a classical free-space optical (FSO) link budget to phase-randomized weak coherent pulse BB84, decoy-state estimation, and composable finite-key postprocessing. The channel interface separates geometric collection, atmospheric extinction, residual pointing, and detector efficiency, and states when common geometric and pointing expressions are approximations. The finite-key output follows the decoy-state analysis of Lim et al., with key- and test-basis counts estimated separately and an infinite-decoy asymptotic reference. The numerical study covers a five-level attenuation sweep, basis- and vacuum-probability sensitivities, a conditional Chernoff comparison, and integer-count Monte Carlo. For 3.33×108 emitted pulses, the Hoeffding-based predicted one-kilobit-per-second distance limits are 2.727, 1.883, 1.472, 1.236, and 0.962 km from very clear to dense-fog parameterizations. These are conditional performance predictions, not experimental security certificates. Satellite, drone, high-altitude-platform, terrestrial, and train links enter through the same interface but require their own propagation, acquisition, and device inputs. The framework integrates established security tools into an engineering procedure without claiming a new security proof or a universal range.
In this paper, we present a novel analysis of the feasibility of quantum key distribution between a LEO satellite and a ground station. First of all, we study signal propagation through a turbulent atmosphere for uplinks and downlinks, discussing the contribution of beam spreading and beam wandering. Then we introduce a model for the background noise of the channel during night-time and day-time, calculating the signal-to-noise ratio for different configurations. We also discuss the expected error-rate due to imperfect polarization compensation in the channel. Finally, we calculate the expected key generation rate of a secure key for different configurations (uplink, downlink) and for different protocols (BB84 with and without decoy states, entanglement-based Ekert91 protocol).
In the absence of technically mature quantum repeaters, losses in optical fibers limit the distance for ground-bound quantum key distribution. One way to overcome these losses is via optical links to satellites, which has been demonstrated in course of the Chinese-Austrian QUESS mission. Though its findings were impressive, such a large-scale project requires massive financial and time resources. We propose a 32x10x10cm³ nanosatellite orders of magnitude cheaper which is able to perform quantum key distribution (QKD) in a trusted-node scenario, using only commercially available components. We have performed a detailed analysis of such a CubeSat mission (“Q³Sat”), finding that cost and complexity can be reduced by sending the photons from ground to satellite, i.e. using an uplink. Calculations have been done for a prepare-and-send protocol (BB84 with decoy pulses) and for a protocol exploiting quantum entanglement (E91), both using polarization as information carrier. We specified the minimum requirements for the sender stations for these two different protocols. Possible orbits have been assessed, regarding both height and ellipticity to maximize link time and minimize losses. Using long-term weather data, we developed a beam model taking into account absorption, turbulence-induced beam divergence and pointing stability of sender and receiver telescope. Using light pollution measurements from space and their spectra, we arrive at maximum expectable noise count rates. We also specify the requirements for clock stability, classical communication speed and computing requirements. Incorporating all these parameters into our model, we arrive at a link budget which we can use to calculate the expected quantum secure key rates. We have also created a preliminary design of such a 3U CubeSat including a detailed size, weight and power budget and a CAD to account for the assembly of the components. Deploying a 10 cm long mirror telescope covering the small surface of the satellite leaves enough space for a polarization analysis module and housekeeping, communication and computing electronics. Polarization analysis can be done via a polarizing beam splitter and single-photon detectors with a cross section small enough to rule out radiation damage. Pointing stability and detumbling is crucial especially for such a small satellite and can be achieved via spinning wheels, achieving a precision in the tilt and yaw axis of 40 mrad. For one such CubeSat, we estimate the quantum secure key to be acquired between two ground stations during one year to be about 13 Mbit when deploying a decoy protocol. A Bell test between ground and satellite would also be feasible. The uplink design allows to keep the more sensitive, computation-intensive and expensive devices on ground. The experiment proposed by us therefore poses a comparably low-threshold quantum space mission. For a two-year lifetime of the satellite, the price per kilobit would amount to about 20 Euro. In large constellations, Q³Sats could be used to establish a global quantum network, which would further lower the cost. Summarizing, our detailed design and feasibility study can be readily used as a template for global-scale quantum communication.
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.