  Entanglement and information are powerful lenses to probe phases transitions
in many-body systems. Motivated by recent cold atom experiments, which are now
able to measure the corresponding information-theoretic quantities, we study
the Mott transition in the half-filled two-dimensional Hubbard model using
cellular dynamical mean-field theory, and focus on two key measures of quantum
correlations: entanglement entropy and mutual information. We show that they
detect the first-order nature of the transition, the universality class of the
endpoint, and the crossover emanating from the endpoint.
