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Understanding how correlations can be used for quantum communicationprotocols is a central goal of quantum information science. While many authorshave linked global measures of correlations such as entanglement or discord tothe performance of specific protocols, in general the latter may require onlycorrelations between specific observables. In this work, we first introduce ageneral measure of correlations for two-qubit states based on the classicalmutual information between local observables. We then discuss the role of thesymmetry in the state's correlations distribution and accordingly provide aclassification of maximally mixed marginals states (MMMS). We discuss thecomplementarity relation between correlations and coherence. By focusing on asimple yet paradigmatic example, i.e., the remote state preparation protocol,we introduce a method to systematically define proper protocol-tailoredmeasures of correlations. The method is based on the identification of thosecorrelations that are relevant (useful) for the protocol. The approach allowson one hand to discuss the role of the symmetry of the correlationsdistribution in determining the efficiency of the protocol, both for MMMS andgeneral two-qubit quantum states, and on the other hand to devise an optimizedprotocol for non-MMMS that can have a better efficiency with respect to thestandard one. The scheme we propose can be extended to other communicationprotocols and more general bipartite settings. Overall our findings clarify howthe key resources in simple communication protocols are the purity of the stateused and the symmetry of correlations distribution.

Two-qubit correlations revisited: average mutual information, relevant (and useful) observables and an application to remote state preparation