Importance of using the averaged mutual information when quantifying quantum objectivity

In the context of quantum objectivity, a standard way to quantify the classicality of a state is via the mutual information between a system and different fractions of its environment. Many of the tools developed in the relevant literature to quantify quantum objectivity via quantum mutual information rely on the assumption that information about the system leaks symmetrically into its environment. In this work, we highlight the importance of taking this assumption into account, and in particular, we analyze how taking nonaveraged quantum mutual information as a quantifier of quantum objectivity can be severely misleading whenever information about the system is encoded into the environment in a nonhomogeneous way. On the other hand, the averaged mutual information always provides results with a clear operative interpretation.