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

Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality