  If there are correlations between two qubits then the results of the
measurement on one of them can help to predict measurement results on the other
one. It is an interesting question what can be predicted about the results of
two complementary projective measurements on the first qubit. To quantify these
predictions the complementary \emph{knowledge excesses} are used. A non-trivial
constraint restricting them is derived. For any mixed state and for arbitrary
measurements the knowledge excesses are bounded by a factor depending only on
the maximal violation of Bell's inequalities. This result is experimentally
verified on two-photon Werner states prepared by means of spontaneous
parametric down-conversion.
