  NMR quantum information processing studies rely on the reconstruction of the
density matrix representing the so-called pseudo-pure states (PPS). An
initially pure part of a PPS state undergoes unitary and non-unitary
(relaxation) transformations during a computation process, causing a "loss of
purity" until the equilibrium is reached. Besides, upon relaxation, the nuclear
polarization varies in time, a fact which must be taken into account when
comparing density matrices at different instants. Attempting to use time-fixed
normalization procedures when relaxation is present, leads to various anomalies
on matrices populations. On this paper we propose a method which takes into
account the time-dependence of the normalization factor. From a generic form
for the deviation density matrix an expression for the relaxing initial pure
state is deduced. The method is exemplified with an experiment of relaxation of
the concurrence of a pseudo-entangled state, which exhibits the phenomenon of
sudden death, and the relaxation of the Wigner function of a pseudo-cat state.
