  We show that the phenomenon of superadditivity of distillable entanglement
observed in multipartite quantum systems results from the consideration of
states created during the execution of the standard end-to-end quantum
teleportation protocol (and a few additional local operations and classical
communication (LOCC) steps) on a linear chain of singlets. Some of these
intermediate states are tensor products of bound-entangled (BE) states, and
hence, by construction possess distillable entanglement, which can be unlocked
by simply completing the rest of the LOCC operations required by the underlying
teleportation protocol. We use this systematic approach to construct both new
and known examples of superactivation of bound entanglement, and first examples
of activation of BE states using other BE states. A surprising outcome is the
construction of noiseless quantum relay channels with no distillable
entanglement between any two parties, except for that between the two end
nodes.
