  In quantum mechanics the statistics of the outcomes of a measuring apparatus
is described by a positive operator valued measure (POVM). A quantum channel
transforms POVM's into POVM's, generally irreversibly, thus loosing some of the
information retrieved from the measurement. This poses the problem of which
POVM's are "undisturbed", namely they are not irreversibly connected to another
POVM. We will call such POVM clean. In a sense, the clean POVM's would be
"perfect", since they would not have any additional "extrinsical" noise. Quite
unexpectedly, it turns out that such cleanness property is largely unrelated to
the convex structure of POVM's, and there are clean POVM's that are not
extremal and vice-versa. In this paper we solve the cleannes classification
problem for number n of outcomes n<=d (d dimension of the Hilbert space), and
we provide a a set of either necessary or sufficient conditions for n>d, along
with an iff condition for the case of informationally complete POVM's for
n=d^2.
