Thermal Operations Involving a Single-mode Bosonic Bath

We study the limitations on coherence evolutions under the constraints of thermodynamic laws, and focus on the optimal thermal operations (TO) reaching the bounds. For qubit case, we find a thermal operation involving only a single-mode reservoir (STO) which maintains the maximum coherence allowed by general TO. For higher dimensions, we derive general bounds on coherence merging under TO, and find STO to reach the bounds. By applying the bound to a two-qubit system, we prove that erasing correlations while preserving the marginal states is not free in the resource theory of thermodynamics. Due to the simple structure of STO and its strong ability in coherence processing, our results shed light on both theoretical and experimental studies in the field of thermodynamics for small quantum systems.