On the spectral dependence of separable and classical correlations in small quantum systems

We study the correlation structure of separable and classical states in 2× 2and 2× 3dimensional quantum systems with fixed spectra. Even for such simple systems the maximal correlation as measured by mutual information over the set of unitarily accessible separable states is highly non-trivial to compute; however for the 2× 2 case a particular class of spectra admits full analysis and allows us to contrast classical states with more general separable states. We analyse a particular entropic binary relation on the set of spectra and prove for the qubit-qutrit case that this relation alone picks out a unique classical maximum state for mutual information. Moreover the 2× 3 case is the largest system with such a property.