  Deficit of information zero-way was proposed in HorodeckiHHOSSS2005 as one of
possible measures of quantumness of correlations. Numerical calculations
suggested that there exist such states for which this quantity is almost equal
to mutual information. In this paper we present a family of states for which we
have equality between above measure of quantumness of correlations and the
measure of total correlations -- mutual information. It means that whole
correlations in these states have, in some sense, quantum character and that
quantum correlations do not necessarily imply classical correlations. We prove
this intriguing feature for a subclass of 2x2 separable states. We also present
numerical result suggesting that this interesting situation might also happen
for 2x2 entangled states.
