## 2 Principle of CVQKD with Coherent States  
By definition, all CVQKD protocols encode information in the quadratures of the quantized electromagnetic field. This information is then recovered thanks to coherent detection techniques, in particular homodyne (or heterodyne) detection of those quadratures. From this perspective, the main distinction between discrete-variable and continuous-variable protocols lies in the detection technique that is employed: single-photon detection for the former and homodyne (or heterodyne) for the latter. A number of CV protocols has been proposed in the literature and depend on the choice of states that are prepared: single-mode coherent or squeezed states, two-mode squeezed states; on the choice of modulation for single-mode states, Gaussian or non-Gaussian; on the choice of detection, homodyne or heterodyne; and finally, on the type of error correction (or else, reconciliation), direct or reverse. Of course, some of these protocols are easier to implement, and some have better security proofs than others. In this review, we will mainly focus on the simplest ones, which are also the best understood ones, namely one-way protocols using a Gaussian modulation. Other protocols have been investigated in the literature: two-way protocols [13, 14], protocols with a non-Gaussian modulation [15, 16, 17, 18, 19] or post-selection [20]; but, their security analysis is less advanced, and we will not consider them further in this short review. As usual with QKD, a given protocol has two possible implementations, prepare and measure (PM) or entanglement based (EB), which are known to be equivalent in the case of Gaussian protocols [21]. In the first case, [PERSON] simply prepares and sends Gaussian states to [PERSON], who measures them with coherent detection; in the second version, [PERSON] generates bipartite entangled states, measures the first half and sends the second half to [PERSON], who measures it. As long as [PERSON]'s lab and preparation is trusted, both variants have the same security. More precisely, the security of the PM version reduces to that of the EB protocol. For this reason, it is only necessary to analyze the security of EB QKD protocols. Implementations, on the other hand, are usually simpler for PM protocols. The simplest CVQKD protocol is certainly GG02 introduced by [PERSON] and [PERSON] in 2002 [22], or its variant with heterodyne detection [23]. We now describe the rough outline of this protocol. A much more detailed description can be found elsewhere [24], but is out of the scope of this paper. The protocol consists of four main steps: (i) state distribution and measurement; (ii) error reconciliation; (iii) parameter estimation; and (iv) privacy amplification. Note that historically, parameter estimation used to be applied before error correction, but the novel order turns out to be more efficient. (i) State distribution and measurement: [PERSON] prepares a large number of coherent states \(|\alpha_{1}\rangle,\ldots,|\alpha_{N}\rangle\), where \(\alpha_{i}\) are independent and identically distributed complex Gaussian variables \(\mathcal{N}_{\mathbb{C}}(0,V_{0})\) with variance \(V_{0}\). Depending on the protocol (homodyne or heterodyne), [PERSON] measures either a random quadrature (\(x\) or \(p\)) for each state and informs [PERSON] of his choices or both quadratures. [PERSON] then obtains a list of \(N\) or \(2N\) real-valued numbers corresponding to his measurement outcomes. [PERSON] has also access to her own list of data (she keeps only the relevant quadrature values if [PERSON] performed a homodyne detection). Denote the respective lists of [PERSON] and [PERSON] by \(x=(x_{1},\ldots,x_{n})\) and \(y=(y_{1},\ldots,y_{n})\) (where \(n\) is either \(N\) or \(2N\)). (ii) Error reconciliation: The protocol achieves in general better performance with reverse reconciliation [25] (except at very short distances [26]): this means that [PERSON]'s string corresponds to the raw key, and [PERSON] tries to guess its value.