Continuous-variable Quantum Key Distribution protocols with a discrete modulation

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In this paper, we consider continuous-variable quantum key distribution with a discrete modulation, either binary or quaternary.

• We establish the security of these protocols against the class of collective attacks that induce a linear quantum channel.
• In particular, all Gaussian attacks are taken into account, as well as linear attacks which add a non-Gaussian noise.
• We give lower bounds for the secret key rate using extremality properties of Gaussian states.