Spectral effects in quantum key distribution

In recent years tremendous research progress was made in the field of quantum key distribution (QKD). By now a variety of protocols exists for which security has been proven even for realistic imperfect devices. The proofs based on the idea of Shor and Preskill, provide us with a lower bound on the secure key generation rate. The security of BB84 relies on the fact, that well defined single-mode photonic states are prepared by the sender and used as information carriers. However, potential sources for QKD implementations like parametric down conversion (PDC) sources emit states with a multi-mode spectral distribution. These states have to be described in a higher-dimensional Hilbert space. We investigate to what extent these spectral properties affect the security considerations. We further present a comparison of the theoretical bounds on the secure key rates for different protocols and the dependence on various experimental imperfections, e.g., dark-counts, detector efficiency, channel attenuation etc. Only single-photon signals contribute to the secure key, but unfortunately such sources don't exist at present. Hence we consider different photon statistics in our simulations