As a consequence of the place ascribed to measurements in the postulates of
quantum mechanics, if two differently prepared systems are described with the
same density operator \r{ho}, they are said to be in the same quantum state.
For more than fifty years, there has been a lack of consensus about this
postulate. In a 2011 paper, considering variances of spin components, Fratini
and Hayrapetyan tried to show that this postulate is unjustified. The aim of
the present paper is to discuss major points in this 2011 article, and in their
reply to a 2012 paper by Bodor and Diosi claiming that their analysis was
irrelevant. Facing some ambiguities or inconsistencies in the 2011 paper and in
the reply, we first try to guess their aim, then establish results useful in
this context, and finally discuss the use or misuse of several concepts implied
in this debate