  We provide an interpretation of entanglement based on classical correlations
between measurement outcomes of complementary properties: states that have
correlations beyond a certain threshold are entangled. The reverse is not true,
however. We also show that, surprisingly, all separable nonclassical states
exhibit smaller correlations for complementary observables than some strictly
classical states. We use mutual information as a measure of classical
correlations, but we conjecture that the first result holds also for other
measures (e.g. the Pearson correlation coefficient or the sum of conditional
probabilities).
