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.
