  We consider the classical correlations that two observers can extract by
measurements on a bipartite quantum state, and we discuss how they are related
to the quantum mutual information of the state. We show with several examples
how complementarity gives rise to a gap between the quantum and the classical
correlations, and we relate our quantitative finding to the so-called classical
correlation locked in a quantum state. We derive upper bounds for the sum of
classical correlation obtained by measurements in different mutually unbiased
bases and we show that the complementarity gap is also present in the
deterministic quantum computation with one quantum bit.
