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 $Ileq E$ 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 Holevos bound.
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