  We analyze the conditions for entanglement amplification between distant and
not directly interacting quantum objects by their common coupling to media with
static modular structure and subject to a local (single-bond) quenched
dynamics. We show that in the non-perturbative regime of the dynamics the
initial end-to-end entanglement is strongly amplified and, moreover, can be
distributed efficiently between distant objects. Due to its intrinsic local and
non-perturbative nature the dynamics is fast and robust against thermal
fluctuations, and its control is undemanding. We show that the origin of
entanglement amplification lies in the interference of the ground state and at
most one of the low-lying energy eigenstates. The scheme can be generalized to
provide a fast and efficient router for generating entanglement between
simultaneous multiple users.
