Quantum key distribution systems based on weak coherent pulses

Quantum key distribution (QKD) is a novel technique that exploits quantum effects to generate a secret key between two distant parties despite the computational and technological power of an eavesdropper who interferes with the signals. After the first demonstration of the practical feasibility of these schemes, several long-distance implementations of QKD have been realized in the last years. In this paper, we present simple upper bounds on the secret key rate and on the quantum bit error rate of two of the most relevant QKD protocols nowadays: decoy state QKD and differential-phase-shift QKD.