2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104100By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can be carried to provide a better understanding of the geometry of entanglement. Surprisingly, this study can be done experimentally, what allows to determine the shape of different entangled states sets, a purely mathematical definition, in real experiments.3 text pages, 7 figures, submited to Nature Physics. V2: Just an aesthetic change! V3: new abstract, references added, shorter introduction - a PRL versionQuantum Physicstext