Rate of lineage origin explains the diversity anomaly in the World’s mangrove vegetation

The contribution of nonecological factors to global patterns in diversity is evident when species richness differs between regions with similar habitats and geographic area. Mangrove environments in the Eastern Hemisphere harbor six times as many species of trees and shrubs as similar environments in the New World. Genetic divergence of mangrove lineages from terrestrial relatives, in combination with fossil evidence, suggests that mangrove diversity is limited by evolutionary transition into the stressful marine environment, the number of mangrove lineages has increased steadily over the Tertiary with little global extinction, and the diversity anomaly in mangrove vegetation reflects regional differences in the rate of origin of new mangrove lineages

An information-theoretic security proof for QKD protocols

We present a new technique for proving the security of quantum key distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the BB84, the six-state, and the B92 protocol with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.Comment: 18 pages, 3 figure