  We study the transferring of useful energy (work) along a transmission line
that allows for partial preservation of quantum coherence. As a figure of merit
we adopt the maximum values that ergotropy, total ergotropy, and
non-equilibrium free-energy attain at the output of the line for an assigned
input energy threshold. For Phase-Invariant Bosonic Gaussian Channels (BGCs)
models, we show that coherent inputs are optimal. For (one-mode) not
Phase-Invariant BGCs we solve the optimization problem under the extra
restriction of Gaussian input signals.
