Applying pressure to water reduces the average oxygen-oxygen distance, and facilitates the delocalisation of protons along the hydrogen bond. This pressure-induced delocalisation is further enhanced by the quantum nature of hydrogen nuclei, which is very significant even well above room temperature. Here we will evaluate the quantum kinetic energy and the particle momentum distribution of hydrogen and oxygen nuclei in water at extreme pressure, using ab initio path integral molecular dynamics. We will show that (transient) dissociation of water molecules induce measurable changes in the kinetic energy hydrogen atoms, although current deep inelastic scattering experiments are probably unable to capture the heterogeneity of the sample.