## 1 Introduction  
The QKD (Quantum Key Distribution) systems represent one of the most important practical applications of quantum information theory [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. The QKD schemes allow for establishing an unconditionally secret communication between distant parties by exploiting the fundamental attributes of quantum mechanics [19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53]. The QKD protocols can be classified into three main classes [1; 2; 3; 4; 50; 51; 52; 53]: DVQKD (Discrete-Variable), CVQKD (Continuous-Variable), and DPR-QKD (Differential Phase Reference) systems. The firstly introduced QKD protocols were based on discrete variables, such as photon polarization. Since the polarization of single photons cannot be encoded and decoded efficiently because of the technological limitations of current physical devices, the CVQKD systems were proposed. In a CVQKD system, the information is encoded on continuous variables by a Gaussian modulation, such as in the position or momentum quadratures of coherent states. In comparison to DVQKD, the modulation and decoding of continuous variables does not require specialized devices and can be implemented efficiently by standard technologies that are available and in widespread use. The CVQKD systems also provide higher secret key rates and higher communication distances. The CVQKD protocols can be further classified into one-way and two-waysystems. In a one-way CVQKD system, [PERSON], the sender transmits her continuous variables to the receiver, [PERSON], over a quantum channel [9; 10; 11]. In a two-way system, [PERSON] starts the communication, [PERSON] adds her internal secret to the received message, and this is then sent back to [PERSON] (e.g., one mode of the coupled beam that is outputted from a beamsplitter is transmitted back to [PERSON]). The two-way CVQKD systems were introduced for practical reasons to exceed the limitations of one-way CVQKD, such as low key rates and short communication distances [1; 2; 3; 4; 5; 6; 7; 8]. The two-way CVQKD protocols exploit the benefits of multiple channel uses and allow for the leak of only lower valuable information to the eavesdropper. On the other hand, the achievable distances of one-way CVQKD can be extended by efficient channel-estimation methods [36], which is important since the one-way protocol currently is still the focus of the research, owing to the easy experimental implementation. The CVQKD schemes use continuous-variable Gaussian modulation, which provably provides optimal key rates against collective attacks at finite-size block lengths [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11] and also maximizes the mutual information between [PERSON] and [PERSON]. The security of CVQKD has also been proven against collective attacks in the asymptotic regime with infinite block sizes, and against arbitrary attacks in the finite-size regime [9; 13; 38; 39; 40]. One of the most critical points in regard to CVQKD is the post-processing [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. The post-processing is aimed to correct the errors of the quantum channel that are cumulated in the raw data. The raw data is a correlated binary bitstring at [PERSON]'s and [PERSON]'s side, as generated by the random quadrature measurements at the parties. Each quadrature measurement results in a unit in the raw data. The raw data itself is not a secret key; it consists only of the results of the random quadrature measurements. The secret key is a uniformly distributed long binary string that will be combined with the raw data elements, and will be added to the picture only in the stage of logical layer manipulations. The logical layer-based post-processing phase uses purely classical tools: precisely a classical-authenticated communication channel and classical error-correction algorithms.