  Since a 1932 work from von Neumann, it is generally considered that if two
statistical mixtures are represented by the same density operator \r{ho}, they
should in fact be considered as the same mixture. In a 1970 paper, Zeh,
considering this result to be a consequence of what he called the measurement
axiom, introduced a thought experiment with neutron spins and showed that in
that experiment the density operator could not tell the whole story. Since
then, no consensus has emerged yet, and controversies on the subject still
presently develop. In this paper, stimulated by our previous works in the field
of Quantum Information Processing, we show that the two mixtures imagined by
Zeh, with the same \r{ho}, should however be distinguished. We show that this
result suppresses a restriction unduly installed on statistical mixtures, but
does not affect the general use of \r{ho}, e.g. in quantum statistical
mechanics, and the von Neumann entropy keeps its own interest and even helps
clarifying this confusing consequence of the measurement axiom. In order to
avoid any ambiguity, the identification of the introduction of this postulate,
which von Neumann rather suggested to be a general property, is given in an
appendix where it is shown that Zeh was right when he spoke of a measurement
axiom and identified his problem. The use and content of a density operator is
also discussed in another physical case which we are led to call the
Landau-Feynman situation, and which implies the concept of entanglement rather
than the one of mixed states.
