We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states which extends into bound entanglement regions. This is done by using an efficiently computable concurrence lower bound, which is further employe
d to numerically construct a volume of $3 times 3$ bound entangled states.
Quantum correlations as the resource for quantum communication can be distributed over long distances by quantum repeaters. In this Letter, we introduce the notion of a noisy quantum repeater, and examine its role in quantum communication. Quantum co
rrelations shared through noisy quantum repeaters are then characterized and their secrecy properties are studied. Remarkably, noisy quantum repeaters naturally introduce private states in the key distillation scenario, and consequently key distillation protocols are demonstrated to be more tolerant.
