Resource speed limits: maximal rate of resource variation

Recent advances in quantum resource theories have been driven by the fact that many quantum information protocols make use of different facets of the same physical features, e.g. entanglement, coherence, etc. Resource theories formalise the role of these important physical features in a given protocol. One question that remains open until now is: how quickly can a resource be generated or degraded? Using the toolkit of quantum speed limits we construct bounds on the minimum time required for a given resource to change by a fixed increment, which might be thought of as the power of said resource, i.e., the rate of resource variation. We show that the derived bounds are tight by considering several examples. Finally, we discuss some applications of our results, which include generalisations of thermodynamic work, heat, and power to any given resource, as well as fundamental bounds on the computation rate in leading quantum processing architectures.