Cascades of gluons at high energies and their QI measures

In this contribution we report on recent extension of one dimensional dipole cascade models to account for saturation and transition to vacuum \cite{Kutak:2025syp}. We analyze properties of the models using Quantum Information tools. Furthermore, we present a description of the hadronic entropy measured by LHCb and predictions for the purity measurement. %we provide description of hadronic entropy as measured by LHCb and provide predictions for measurement of purity.