Hot carriers produced from the decay of localized surface plasmons in metallic nanoparticles are intensely studied because of their optoelectronic, photovoltaic and photocatalytic applications. From a classical perspective, plasmons are coherent oscillations of the electrons in the nanoparticle, but their quantized nature comes to the fore in the novel field of quantum plasmonics. In this work, we introduce a quantum-mechanical material-specific approach for describing the decay of single quantized plasmons into hot electrons and holes. We find that hot carrier generation rates differ significantly from semiclassical predictions. We also investigate the decay of excitations without plasmonic character and show that their hot carrier rates are comparable to those from the decay of plasmonic excitations for small nanoparticles. Our study provides a rigorous and general foundation for further development of plasmonic hot carrier studies in the plasmonic regime required for the design of ultrasmall devices.