## 4 Experimental Implementations
These implementations, together with a few others [56, 57, 58, 59], were suited for securing communications in metropolitan area size networks (involving distances up to 25 km) with high-speed requirements. Although there are several interesting applications of short-range experiments, from a quantum information network point of view, it is important to be able to extend the communication distance beyond this limit. In discrete-variable QKD implementations, the distance limitation is essentially determined by the characteristics of single-photon detectors, and in particular their dark counts. In CVQKD, it used to be the efficiency of the complex post-processing techniques that limited the range. Although this is no longer the case, it is instructive to understand the origin of this limitation: the efficient reconciliation of correlated Gaussian variables is in fact hard, especially at low signal-to-noise (SNR) ratios, which are inherent in long-distance experiments, hence reducing the \(\beta\) factor introduced in Section 3. An an indicative value, \(\beta=0.9\) was achieved for an SNR = 3 (at Bob's site) in the aforementioned experiments. In recent years, a series of works successfully addressed this issue leading to the development of highly-efficient error-correcting codes at low SNR. These combine multidimensional reconciliation techniques [60] with efficient multi-edge low density parity check (LDPC) codes [61] and can also be optimized for short distances [26]. With these codes, it is possible to reach, for example, an efficiency \(\beta=0.96\) at SNR = 0.075, opening the way to experiments over significantly longer distances. We note that with the help of non-binary LDPC codes, similar efficiencies can also be obtained for higher values of the SNR [62]. In addition to error correction, the parameter estimation procedure is also crucial for the extraction of the secret key in practice. For the optical setup of Figure 1, the relevant experimental parameters are Alice's modulation variance \(V_{A}\), the channel transmittance \(T\) and the excess noise \(\xi\), which is the noise added by the channel beyond the fundamental shot noise and corresponds to the usual quantum bit error rate found in discrete-variable QKD implementations. Both \(V_{A}\) and \(\xi\), are typically expressed in shot noise units. The parameter \(V_{A}\) is adjusted in real time in order to be at all times as close as possible to the SNR corresponding to the threshold of an available error correcting code, while the parameters \(T\) and \(\xi\), need to be estimated in real time by randomly revealing a fraction of the samples. Two additional experimental parameters that are used to compute an estimate of the secret information that can be extracted from the shared data are the electronic noise \(v_{\mathrm{el}}\) and the efficiency \(\eta\) of the homodyne detection. In the so-called realistic CVQKD scenario, these are assumed to not be accessible to [PERSON] and are measured during a secure calibration procedure that takes place before the deployment of the system. In general, however, these parameters may be available to [PERSON]. The parameter estimation procedure allows one to compute bounds for the eavesdropper's information, taking calibrated value uncertainties into account [63]. Following error reconciliation and parameter estimation, privacy amplification allows extracting the secret information from the identical strings shared by [PERSON] and [PERSON]. For the scheme of Figure 1, the upper bound on [PERSON]'s information on the corrected string can be computed for collective attacks in both the asymptotic regime [30,31], where all of the experimental parameters are assumed to be known with an infinite precision, and in the finite-size regime, where the parameters are estimated over large, but finite data pulse sets [63] (see Section 3 for rigorous security definitions).