2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91915Generalizing the notion of relative entropy, the difference between a priori and a posteriori relative entropy for quantum systems is drawn. The former, known as quantum relative entropy, is associated with quantum states recognition. The latter -- a posteriori relative quantum entropy is shown to be related with state reconstruction due to the following property: given a density operator $ρ$, ensembles of pure states with Gibbs distribution with respect to the defined distance are proved to represent the initial state $ρ$ up to an amount of white noise (completely mixed state) which can be made arbitrary small.LaTeX 2e, 3 PS figures, 4 pages + 3 pages appendixQuantum Physicstext