2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187351In this paper it was proved that the quantum relative entropy $D(σ\| ρ)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $ρ$, but is independent of the choice of $σ$.LaTeX2e. 8 pages. The title was changed from "Asymptotic Attainment for Quantum Relative Entropy"Quantum Physicstext