Role of energy-invariant assistants in energy extraction from quantum batteries

We investigate the role of energy-invariant assistants in energy extraction from quantum batteries. To this end, for energy extraction, we restrict to unitaries that jointly act on the battery and the assistant but keep the assistant’s energy preserved. We demonstrate that in the presence of an energy-invariant assistant, having the same dimension as the battery, all stored energy of the battery can always be extracted, transforming the battery into its ground state, when an appropriate joint unitary and assistant’s state are employed. Additionally, we offer a necessary and sufficient condition for a battery to be unable to provide any energy, i.e. to be inactive, even when an energy-invariant assistant is present, prepared in an arbitrary but fixed state.