This WP investigates the geometric structure of information spaces in classical and quantum systems, with applications (stabilizer code). It will focus on symmetry-invariant geometric structures on spaces of quantum states, establishing strong links with the representation-theoretic and symmetry-based results of WG1. It will also develop novel geometric tools for the detection, characterization and quantification of quantum correlations, via a quantum generalization of information geometric methods. It will exploit the language of integrable systems to the theoretical design of quantum circuits.