Exploring the gap between thermal operations and enhanced thermal operations

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. We analytically calculate the coherence under TO for a given class of population dynamics, and observe a non-negligible gap between the maximum coherence under TO and that under EnTO. By the Stinespring dilation theorem, one can simulate any EnTO with TO by using an auxiliary system which is non-equilibrium but contains no coherence. Interestingly, we prove that the gap cannot be narrowed as long as the auxiliary state is full-rank. Also, we evaluated the amount of work which is required for simulating EnTO by TO. Our results contribute to the research of coherence dynamics in quantum thermodynamics.

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