While we now have a complete picture of the average local and intermediate structures of the various amorphous ices, their dynamic behaviour (glass transition and defect migration) and the classification into distinct states are still debated. Ultimately, definitive answers may only be found with a more detailed knowledge of the low-temperature potential energy landscape of water. This proposal is part of a theoretical and experimental characterization programme of the proton quantum states in the condensed water phases which include: a series of inelastic experiments as well as theoretical simulations (Ab-Initio Path Integral Molecular Dynamics). The MARI data together with the AIPIMD simulations and DINS experiments on VESUVIO will provide unique information on the proton quantum dynamics of the amorphous ices from the intermolecular and intramolecular vibrations up to the DINS regime.