  We show that the metastable, symmetry-breaking ground states of quantum
many-body Hamiltonians have vanishing quantum mutual information between
macroscopically separated regions, and are thus the most classical ones among
all possible quantum ground states. This statement is obvious only when the
symmetry-breaking ground states are simple product states, e.g. at the
factorization point. On the other hand, symmetry-breaking states are in general
entangled along the entire ordered phase, and to show that they actually
feature the least macroscopic correlations compared to their symmetric
superpositions is highly non trivial. We prove this result in general, by
considering the quantum mutual information based on the $2-$R\'enyi
entanglement entropy and using a locality result stemming from quasi-adiabatic
continuation. Moreover, in the paradigmatic case of the exactly solvable
one-dimensional quantum $XY$ model, we further verify the general result by
considering also the quantum mutual information based on the von Neumann
entanglement entropy.
