  We introduce new measures of multipartite quantum correlations based on
classical correlations in mutually unbiased bases. These classical correlations
are measured in terms of the classical mutual information, which has a clear
operational meaning. We present sufficient conditions under which these
measures are maximized. States that have previously been shown to be
particularily important in the context of LOCC transformations fulfill these
conditions and therefore maximize the correlation measures. In addition, we
show how the new measures can be used to detect high-dimensional tripartite
entanglement by using only a few local measurements.
