Exploring the gap between thermal operations and enhanced thermal operations

Abstract: The gap between thermal operations (TO) and enhanced thermal operations (EnTO) is an open problem raised in [Phys. Rev. Lett. 115, 210403 (2015)]. It originates from the limitations on coherence evolutions. Here we solve this problem by analytically proving that, a state transition induced by EnTO cannot be approximately realized by TO. It confirms that TO and EnTO lead to different laws of state conversions. Our results can also contribute to the study of the restrictions on coherence dynamics in quantum thermodynamics.