Strategies of Legitimate Parties and an Eavesdropper for Discretely Modulated Continuous-Variables Quantum Key Distribution Protocols

Discretely modulated continuous-variables quantum key distribution (CV-QKD) protocols are usually proposed with phase modulated coherent states being sent by Alice and simple homodyne detection on the Bob side and, in the majority of the studies, their security is analyzed assuming that for low photon number the protocols are similar to a Gaussian modulated CV-QKD. Here we discuss other detection techniques such as double homodyne, consider classical attacks and find practical strategies for the legitimate parties to reach the security limits predicted by the Gaussian modulated CV-QKD.