A note on continuous ensemble expansions of quantum states
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:quantph/0403105
 Bibcode:
 2004quant.ph..3105Z
 Keywords:

 Quantum Physics
 EPrint:
 LaTeX 2e, 3 PS figures, 4 pages + 3 pages appendix