Indium phosphide quantum dots are the main alternative for toxic and restricted Cd-based quantum dots for lighting and display applications, but in the absence of protecting ZnSe and/or ZnS shells, InP quantum dots suffer from low photoluminescence quantum yields. Traditionally, HF treatments have been used to improve the quantum yield of InP to ~50%, but these treatments are dangerous and not well understood. Here, we develop a postsynthetic treatment that forms HF in situ from benzoyl fluoride, which can be used to strongly increase the quantum yield of InP core-only quantum dots. This treatment is water-free and can be performed safely. Simultaneous addition of the z-type ligand ZnCl2 increases the photoluminescence quantum yield up to 85%. Structural analysis via XPS as well as solid state and solution NMR measurements shows that the in situ generated HF leads to a surface passivation by indium fluoride z-type ligands and removes polyphosphates, but not PO3 and PO4 species from the InP surface. With DFT calculations it is shown that InP QDs can be trap-free even when PO3 and PO4 species are present on the surface. These results show that both polyphosphate removal and z-type passivation are necessary to obtain high quantum yields in InP core-only quantum dots. They further show that core-only InP QDs can achieve photoluminescence quantum yields rivalling those of InP/ZnSe/ZnS core/shell/shell QDs and the best core-only II-VI QDs.