Universality and classification of elementary thermal operations

Abstract: Elementary thermal operations are thermal operations that act non-trivially on at most two energy levels of a system at the same time. They were recently introduced in order to bring thermal operations closer to experimental feasibility. A key question to address is whether any thermal operation could be realized via elementary ones, that is, whether elementary thermal operations are universal. This was shown to be false in general, although the extent to which elementary thermal operations are universal remained unknown. Here, we characterize their universality in both the sense described above and a weaker one, where we do not require them to decompose any thermal operation, but to be able to reproduce any input-output pair connected via thermal operations. Moreover, we do so for the two variants of elementary thermal operations that have been proposed, one where only deterministic protocols are allowed and one where protocols can be conditioned via the realization of a random variable, and provide algorithms to emulate thermal operations whenever their elementary counterparts are (weakly or not) universal. Lastly, we show that non-deterministic protocols reproduce thermal operations better than deterministic ones in most scenarios, even when they are not universal. Along the way, we relate elementary thermal operations to random walks on graphs.