# Semi-Empirical Satellite-to-Ground Quantum Key Distribution Model for Realistic Receivers
###### Abstract  
Satellite-based link analysis is valuable for efficient and secure quantum communication, despite seasonal limits and restrictions on transmission times. A semi-empirical quantum key distribution model for satellite-based systems was proposed that simplifies simulations of communication links. Unlike other theoretical models, our approach was based on the experimentally-determined atmospheric extinction coefficient typical for mid-latitude ground stations. The parameter was measured for both clear and foggy conditions, and it was validated using published experimental data from the Micius satellite. Using this model, we simulated secure QKD between the Micius satellite and ground stations with 300 mm and 600 mm aperture telescopes.  
satellite quantum communication; quantum key distribution; optical communication; free-space optics; quantum channel modeling +
Footnote †: journal: _Entropy_  
002333  
satellite, and successfully demonstrated satellite-to-ground QKD via polarization photon states [13; 14].  
As a promising concept, the first quantum science satellite paved the way for a future global quantum network, enabling secure worldwide data transfer [15; 16; 17]. Meanwhile, as a communication network capable of providing secret keys as a service, industrial quantum key distribution networks must meet the core requirements of flexible extension, cost effectiveness, component compatibility, and standardization [18; 19; 20; 21]. As a result, a strict and comprehensive analysis of a quantum communication channel is needed to build an efficient quantum network [22; 23], despite seasonal limits and restrictions on transmission times between satellites and ground stations.  
Satellite-based uplink-downlink [24] and measurement-device-independent QKD models [25] were proposed recently. Additionally, a theoretical analysis of the quantum communication link between the Micius satellite and the Delingha receiving ground station was performed [22; 26]. The existing theoretical models are valuable for a comprehensive analysis of free-space QKD. However, these models take into consideration many factors not known with sufficient accuracy, such as air turbulence, background noise, and pointing and tracking losses [8], which significantly limit their practical usage.  
In this paper, we present a semi-empirical satellite-to-ground QKD model relying on phenomenological data by employing atmospheric extinction measurements. This allows for a realistic analysis of developed ground stations with 300 and 600 mm telescope apertures in terms of secure key rate and error rate. Considering our simulation of experimental results obtained with Micius [13] and a theoretical model [8; 22], a more relevant and real range of sifted key rate for the satellite-based QKD was provided.  
This paper is organized as follows: in Section 2, we describe the communication channel geometry for a series of satellite passages over Zvenigorod observatory and computed the time-dependent distance between the satellite and ground stations; in Section 3, we calculated overall link losses based on the measured characteristics of ground stations [27] and the photon source parameters of a satellite [13]; Section 4 examined the secure key generation and error rates of QKD systems using the standard BB84 decoy-state protocol [28; 29]; finally, in Section 5, we discuss the deployment of our model to future space-to-ground quantum communication experiments.