Periodic Reporting for period 1 - SatCV (Satellite CV-QKD) Reporting period: 2019-06-01 to 2021-05-31 Summary of the context and overall objectives of the project It is not necessary to underline the importance of secure data transmission in modern society: from financial and diplomatic transactions to private messages between citizens, almost every aspect of our life depends on this. At present, the security of these communications relies on the hardness of some computational problems, such as number factorization or the discrete logarithm. However, these problems are known to be efficiently solved by a quantum computer, opening a security issue due to the huge recent advancement in this technology. Two possible solutions have been proposed against this problem. The first consists in finding problems that are computationally hard also on a quantum computer, giving rise to the so called post-quantum cryptography. These algorithms are quite inefficient and their hardness on a quantum computer is not proven, but assumed from the non-existence of efficient algorithms to solve them. The second approach consists on using protocols that exploit the quantum properties of light to prove the security of the transmission. These protocols represent the basis of quantum communication.This project is focused on the study of a particular quantum communication protocol, quantum key distribution (QKD), a protocol that allows two parties to exchange cryptographic keys in an unconditionally secure way, i.e. secure against an adversary with infinite computational power. The security of quantum key distribution protocols relies on the presence, in quantum systems, of incompatible physical properties. By choosing randomly the property in which the information is encoded, it is possible to gain an advantage with respect to an adversary who is trying to eavesdrop the communication. The properties this project takes into account are the quadratures of the electromagnetic field, i.e. the amplitude of the sinus and cosinus part of the field, which, in the limit of low intensities, are incompatible. Since these properties can take any value in the real line, they are called continuous variables (CV).The quadratures of the field are widely used for the encoding of information in optical communication. This favored the development of devices and techniques aimed at increasing the communication rate. Part of this project is aimed at studying how to exploit these techniques to increase the rate of QKD using continuous variables. This task requires both a precise definition of the way data are encoded before being transferred and a careful characterization of all the noise sources of the different devices, something that is not necessary for classical communication and that is therefore not so well studied.In addition to this, the use of quantum properties for the encoding of the information makes this communication technique very sensitive to the losses in the channel. Indeed, the information encoded in incompatible physical properties cannot be amplified without being irremediably corrupted. This makes it challenging to extend it to long distances, especially using optical fibers, where losses increase exponentially with distance. For this reason, quantum communication with satellites seems to be the only reasonable technique to extend this communication paradigm at a international or intercontinental level. The second part of this project is aimed at studying the possibility of extending continuous variable QKD to satellites. To this goal, it will be fundamental the interaction with other research groups, that work on the improvement of optical communications with satellites exploiting active ways for correcting the effects of the atmosphere. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far The action has focused mainly on two principal matters: the study of the atmospheric channel and the study and construction of a CV-QKD system. The third part of the action, focused on the experimental test of the CV-QKD system on a simulated atmospheric channel, has not been completed because of the delays due to the pandemic, but it is foreseen in the near future.During the first part of the action, the tools for the analysis of the free-space channel have been developed, using the data acquired during the experiments performed just before the beginning of the action. These tools exploited a semi-analytic model of the coupling efficiency in the low turbulence regime to calculate the turbulence parameters from the coupling histograms. Subsequently, the investigations focused on the study of the satellite-to-ground channel, first by evaluating the effects of adaptive optics on discrete variable (DV) and CV-QKD, in collaboration with the French Aerospace Lab (ONERA), then by implementing a model for the free-space and the satellite-to-ground channel for the NetSQUID simulation software, in collaboration with the TU Delft.The study and construction of a CV-QKD system was focused first on the setup of the hardware, with the characterization of the transmitter and of different coherent receivers. One of the key concepts of the system was the use of digital signal processing (DSP) techniques derived from coherent optical communications, which are characterized by similar setup and working principles. This, however, led to the discovery of a lack of theoretical investigation on those techniques, with respect to the aspects of interest for quantum communication. Indeed, while the aim of classical communication is to decrease the bit error rate (BER), CV quantum communication bases it security on monitoring the noise in a single-mode of the electromagnetic field. Since the pulse-shaping functions used in optical communications are different for those used in previous CV-QKD experiments, it is necessary to carefully study them in order to correctly apply the existing security proofs of CV-QKD.The results of the first part of the action are leading to the preparation of some manuscripts that will be sent to peer-reviewed journals. The research on CV-QKD performed during this action, on the other hand, is not mature enough to give a publication. However, the preliminary results obtained in the last months of the action are very promising and they could be of interest for both the scientific and the industrial community. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) Since the launch of the Chinese satellite Micius, there is a wide interest, among the industry and in government agencies, for satellite quantum communication. However, the design of satellite quantum communication systems require a careful modeling of the atmospheric channel, in order to assess their performance in the mission planning phase. The study of the effects of adaptive optics for different QKD systems is of primary importance for the engineering of such systems, giving useful insight on the complexity of the ground station required to meet the desired communication performance. Therefore, this research is fundamental to make Europe recover its disadvantage with respect to China in this technological domain.Similar importance lies in the study of high-speed CV-QKD, which could represent a cost-effective way to implement QKD and could contribute to its spread. Indeed, this quantum communication scheme uses the same devices found in any fiber optical communication system, so it can take advantage of all the technological improvements in this highly active research field. Moreover, the application of digital signal processing (DSP) techniques to CV-QKD could allow to increase the transmission rate up to the electronic limits of the devices. Artistic view of an optical communication satellite. No copyright restrictions.