  The quantum entanglement $E$ of a bipartite quantum Ising chain is compared
with the mutual information $I$ between the two parts after a local measurement
of the classical spin configuration. As the model is conformally invariant, the
entanglement measured in its ground state at the critical point is known to
obey a certain scaling form. Surprisingly, the mutual information of classical
spin configurations is found to obey the same scaling form, although with a
different prefactor. Moreover, we find that mutual information and the
entanglement obey the inequality $I\leq E$ in the ground state as well as in a
dynamically evolving situation. This inequality holds for general bipartite
systems in a pure state and can be proven using similar techniques as for
Holevo's bound.
