2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120892We consider the action of the group of local unitary transformations, U(m) x U(n), on the set of (mixed) states W of the bipartite m x n quantum system. We prove that the generic U(m) x U(n)--orbits in W have dimension m^2+n^2-2. This problem was mentioned (and left open) by Kus and Zyczkowski in their paper Geometry of entangled states. The proof can be extended to the case of arbitrary finite-dimensional multipartite quantum systems.5 pages. The spelling of author's name correctedQuantum Physicstext