Underlining some limitations of the statistical formalism in quantum mechanics: Reply to the Comment of Bodor and Di\'osi

In a paper of us, it is showed that Density Matrices do not provide a complete description of ensembles of states in quantum mechanics, since they lack measurable information concerning the preparation of the ensembles. Bodor and Di\'osi have later posted a comment on that article, which agrees on some points of it but disagrees on some others. This reply is intended to clarify the discussion.