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 nonequilibrium free energy attain at the output of the line for an assigned input energy threshold. For phase-invariant bosonic Gaussian channel (BGC) 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.

• Received 26 April 2021
• Revised 22 July 2021
• Accepted 21 October 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.210601