Non-unique decompositions of mixed states and deterministic energy transfers

We investigate the impact of non-unique decompositions of mixed states on energy transfer. Mixed states generally have non-unique decompositions into pure states in quantum theory and, by definition, in other non-classical 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 non-unique 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. As a paradigmatic example, we model the source as an EM mode transferring energy to a 2-level system harvester via the Jaynes-Cummings model. We show that the set of coherent EM mode states with fixed $|α|$ that jointly achieve deterministic energy transfer can be expanded to include all mixtures and superpositions of those states. More generally, the results link the defining feature of a non-classical probability theory with the ability to achieve energy transfer without entropy transfer.