Understanding how correlations can be used for quantum communication
protocols is a central goal of quantum information science. While many authors
have linked global measures of correlations such as entanglement or discord to
the performance of specific protocols, in general the latter may require only
correlations between specific observables. In this work, we first introduce a
general measure of correlations for two-qubit states based on the classical
mutual information between local observables. We then discuss the role of the
symmetry in the state's correlations distribution and accordingly provide a
classification of maximally mixed marginals states (MMMS). We discuss the
complementarity relation between correlations and coherence. By focusing on a
simple yet paradigmatic example, i.e., the remote state preparation protocol,
we introduce a method to systematically define proper protocol-tailored
measures of correlations. The method is based on the identification of those
correlations that are relevant (useful) for the protocol. The approach allows
on one hand to discuss the role of the symmetry of the correlations
distribution in determining the efficiency of the protocol, both for MMMS and
general two-qubit quantum states, and on the other hand to devise an optimized
protocol for non-MMMS that can have a better efficiency with respect to the
standard one. The scheme we propose can be extended to other communication
protocols and more general bipartite settings. Overall our findings clarify how
the key resources in simple communication protocols are the purity of the state
used and the symmetry of correlations distribution.Comment: Revised Figures, improved notation and clearer text to better
highlight the main finding
