Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack

Quantum key distribution can be performed with practical signal sources such as weak coherent pulses. One example of such a scheme is the Bennett–Brassard protocol that can be implemented via polarization of the signals, or equivalent signals. It turns out that the most powerful tool at the disposition of an eavesdropper is the photon-number splitting attack. We show that this attack can be extended in the relevant parameter regime so as to preserve the Poissonian photon number distribution of the combination of the signal source and the lossy channel.