  Generalizing 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 $\rho$, ensembles of pure states with Gibbs distribution with
respect to the defined distance are proved to represent the initial state
$\rho$ up to an amount of white noise (completely mixed state) which can be
made arbitrary small.
