Quantum Energy Lines and the optimal output ergotropy problem

TL;DR

This paper investigates the optimal transfer of quantum energy along a transmission line, focusing on maximizing ergotropy and free energy at the output, with specific results for phase-invariant and non-phase-invariant Bosonic Gaussian Channels.

Contribution

It provides the first analysis of energy transfer optimization in quantum channels considering coherence preservation and solves the problem for Gaussian inputs in non-phase-invariant channels.

Findings

Coherent inputs are optimal for phase-invariant Bosonic Gaussian Channels.

Optimal energy transfer is characterized by maximum ergotropy and free energy at the output.

Solutions are provided for Gaussian inputs in non-phase-invariant channels.

Abstract

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.