Nonunique Decompositions of Mixed States and Deterministic Energy Transfers

We investigate the impact of nonunique decompositions of mixed states on energy transfer. Mixed states generally have nonunique decompositions into pure states in quantum theory and, by definition, in other nonclassical probabilistic theories. We consider energy transfers constituting deterministic energy harvesting, wherein the source transfers energy to the harvester but not entropy. We use the possibility of nonunique decompositions to derive that, if source states in a set jointly lead to deterministic energy harvesting for the given harvesting system and interaction, then that set can be expanded to include both mixtures and superpositions of the original states in the set. In the Jaynes-Cummings model, we show that source states supported on specific Fock states and their superpositions achieve exact deterministic energy harvesting, while coherent states with fixed |α| and their superpositions achieve approximate deterministic energy harvesting. More generally, the results link the defining feature of a nonclassical probability theory with the ability to achieve energy transfer without entropy transfer.