# Wavelength Selection for Satellite Quantum Key Distribution
## 1 Introduction  
The security of the Internet depends on public-key (asymmetric) cryptography and the inability of computers to solve particular types of computationally intense problems in a short amount of time. Quantum algorithms enabled by quantum computers pose a serious threat to this type of encryption. [PERSON]'s algorithm can factor large integers in polynomial time and could theoretically be used to break many public-key cryptography schemes [1]. This has led researchers to investigate ways to enable quantum-safe data transmission. One of the most promising methods is quantum key distribution (QKD), which uses quantum physics to enable the secure exchange of symmetric cryptography keys between two parties by detecting the presence of an eavesdropper during the exchange [2, 3, 4]. Despite QKD being one of the most mature quantum technologies, it still lacks the infrastructure to establish a global quantum-safe network. The most common classical communication channel is optical fibre, which can efficiently carry information around the globe by using amplifiers to boost the signal as it travels. In quantum communication, the no-cloning theorem prevents the use of amplifiers [5], causing the probability of the qubit being absorbed or depolarised growing exponentially with the length of the fibre. The current distance limitation of fibre optic networks for QKD highlights the need to find alternative transmission methods, such as quantum repeaters, photonic crystal fibre and satellite QKD networks. Quantum repeaters work by dividing the communication distance into smaller regions where keys are separately distributed to each region, followed by entanglement exchange and a purification process that links adjacent nodes [6, 7]. Hollow core fibre (HCF) offers substantial reductions in nonlinear effects and fibre attenuation [8]. Attenuation in HCF has reduced from 0.174 dB/km [9] to below 0.11 dB/km [10]. This significant reduction in attenuation holds potential for future integrated optical communication systems and long distance quantum communication. An alternative solution is to use FSOC to establish a satellite-Earth link, as demonstrated by the Micius satellite [11; 12], which successfully distributed a key over a distance of 1200 km. Although satellite-Earth FSOC shows promise for long-distance (>1000 km) QKD, it faces several practical challenges [13; 14; 15; 16; 17; 18], for example, background noise caused by solar radiation, which makes daytime operation very difficult [19; 20; 21]. [PERSON] et al. have suggested that narrow filtering techniques combined with adaptive optics could permit daytime operation [22; 23]. Another option is to use wavelengths with significant dips in solar radiance, such as those in the mid-wavelength infrared (MWIR) region. Most FSOC and QKD systems operate using wavelengths between 700 nm and 1550 nm [19; 24; 25] due to the abundance of optical components and the overlap with the telecommunication industry. However, limited operational availability due to high attenuation in poor weather conditions has motivated researchers to look at longer wavelengths [26; 27] where authors predict improvements in propagation through fog and turbulence [28; 29]. Advancements in quantum cascade laser technology have enabled researchers to begin investigating the potential advantages of long-wave FSOC and QKD [27; 30; 31]. There are two primary approaches to QKD protocols, continuous-variable (CV) and discrete-variable (DV), with various implementations within each [32; 33]. In the DV scheme, information is encoded in discrete quantum properties of the photon, such as polarization. Alternatively, in the CV scheme, information is encoded in the continuous quadrature variables of the electromagnetic field, such as amplitude and phase of the laser light. In short, DV protocols are considered to be more robust over longer distances than CV protocols, whereas CV protocols have higher key rates [14; 18].