# Parameter Optimization Based BPNN of Atmosphere Continuous-Variable Quantum Key Distribution
## 1 Introduction  
The flying start of quantum communication makes secure communication conceivable in practice [1; 2; 3]. As an important applicatory ahibition in the quantum communications, quantum key distribution (QKD) permits communication objects to generate a public secret key at the existence of eavesdropping, and this approach implements secure key interchange that does not rely on computational complexity [4; 5; 6; 7; 8; 9]. Discrete-variable quantum key distribution (DVQKD) as well as continuous-variable quantum key distribution (CVQKD) are two primary ways to implement QKD. DVQKD protocol demands greatly faint light pulses in the process of generation and detection [5; 6]. Another method of protocol, CVQKD, can utilize standard components of fiber optic communication without the need for a single photon detector [7; 8; 9; 10]. Nowadays, QKD has entered a new stage of development with the goal of widespread application and adoption under a variety of environmental conditions. Long distance QKD in the atmospheric turbulence channel has been realized [11; 12; 13]. Experimental advances in this field have enabled the transmission of quantum light over horizontal communication links to be shown to be successful [14; 15; 16; 17; 18; 19], and the satellite-to-ground DVQKD has been confirmed to exceed 1200 km [20]. Schemes employing single-photon detectors are influenced by background noise [21]; at the same time, coherent detection uses a bright local oscillator (LO) operating as a filter to decrease the background noise [22]. In the process of atmospheric propagation, the beam as a whole experiences random broadening, deformation and random deflection. The main influence comes from the turbulence fluctuation of a refractive index. In addition, the beam can be weaken by backward scattering and absorption. For weakturbulence, the atmosphere mainly causes beam wandering, and this case may be well depicted by the log-negative Weibull distribution [23], while, for moderate and strong turbulence, the beam will be stretched and deformed to form a smooth probability distribution of the transmittance (PDT). In addition, the elliptic-beam model gives consistent results with this situation [24]. Furthermore, this model can also be employed to analyze atmospheric quantum channels under different weather circumstances [25]. The secure key rate depends on the modulation variance, transmittance and excess noise. Unlike optical fiber channels, atmospheric channel transmittance is affected by many factors and does not vary linearly. Therefore, it is crucial to select a suitable modulation variance for different turbulence intensities. This is a kind of a parameter optimization that could guarantee the system security and make the system performance optimal. Previously, to obtain the optimal parameters, it always recurred to simulation and iteration. With enough time and iteration in advance, the approach is mature and accurate [26; 27]. Nevertheless, emulators often consume a large amount of time, notably when running optimizers, which must be repeated many times. Parameter optimization becomes more complex when we extend point-to-point communication to communication networks. Machine learning provides formidable implements for settling matters in many fields, such as estimating parameters, output forecast on the basis of previous input data, data sorting, and pattern identification [28; 29]. In recent years, machine learning technology has been diffusely used both in coherent optical communication [30; 31; 32; 33; 34] and QKD systems [35; 36; 37; 38; 39]. The support vector regression (SVR) is applied to predict the time-along intensity evolutions of the laser light and the LO pulse to improve system performance [35]. In addition, for parameter optimization, this has been done with machine learning in measurement-device-independent (MDI) DVQKD [38; 39]. Hence, the above-mentioned methods provide an idea for parameter optimization in CVQKD at the atmospheric turbulence channel.