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In the context of quantum objectivity, a standard way to quantify theclassicality of a state is via the mutual information between a system anddifferent fractions of its environment. Many of the tools developed in therelevant literature to quantify quantum objectivity via quantum mutualinformation rely on the assumption that information about the system leakssymmetrically into its environment. In this work, we highlight the importanceof taking this assumption into account, and in particular, analyse how takingnon-averaged quantum mutual information as a quantifier of quantum objectivitycan be severely misleading whenever information about the system is encodedinto the environment in a non-homogeneous way. On the other hand, the averagedmutual information always provides results with a clear operativeinterpretation.

The importance of using the averaged mutual information when quantifying quantum objectivity