Abstract
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.