  It was shown that if in Quantum Theory a fundamental length exists and a
well-known measurement procedure is used, then the density matrix at the Planck
scale cannot be defined in the usual way, because in this case density matrix
trace is strongly less than one.
  Density matrix must be changed by a progenitrix or as we call it throughout
this paper, density pro-matrix. This pro-matrix is a deformed density matrix,
which at low energy limit turns to usual one.
  Below the explicit form of the deformation is described. Implications of
obtained results are summarized as well as their application to the
interpretation of Information Paradox on the Black Holes.
