2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162027Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describes such correlations? We introduce the concept of dimension witness to put lower bounds on d. This work represents a first step in a broader research program aiming to characterize Hilbert space dimension in various contexts related to fundamental questions and Quantum Information applications.4 pages, 1 figure; Accepted for publication in PRLQuantum Physicstext