2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/92423Recent developments in mathematics have provided powerful tools for comparing the eigenvalues of matrices related to each other via a moment map. In this paper we survey some of the more concrete aspects of the approach with a particular focus on applications to quantum information theory. After discussing the connection between Horn's Problem and Nielsen's Theorem, we move on to characterizing the eigenvalues of the partial trace of a matrix.40 pages. Accepted for publication in Annals of PhysicsQuantum Physicstext