  The possibility to directly measure, in a cold-atom quantum simulator, the
von Neumann entropy and mutual information between a site and its environment
opens new perspectives on the characterization of the Mott-Hubbard
metal-insulator transition, in the framework of quantum information theory. In
this work we provide an alternative view of the Mott transition in the
two-dimensional Hubbard model in terms of rigorous quasilocal measures of
entanglement and correlation between two spatially separated electronic
orbitals, with no contribution from their environment. A space-resolved
analysis of cluster dynamical mean-field theory results elucidates the
prominent role of the nearest-neighbor entanglement in probing Mott
localization: both its lower and upper bounds sharply increase at the
metal-insulator transition. The two-site entanglement beyond nearest neighbors
is shown to be quickly damped as the inter-site distance is increased. These
results ultimately resolve a conundrum of previous analyses based on the
single-site von Neumann entropy, which has been found to monotonically decrease
when the interaction is increased. The quasilocal two-site entanglement
recovers instead the distinctive character of Mott insulators as strongly
correlated quantum states, demonstrating its central role in the $2d$ Hubbard
model.
