  We compute the leading contribution to the mutual information (MI) of two
disjoint spheres in the large distance regime for arbitrary conformal field
theories (CFT) in any dimension. This is achieved by refining the operator
product expansion method introduced by Cardy \cite{Cardy:2013nua}. For CFTs
with holographic duals the leading contribution to the MI at long distances
comes from bulk quantum corrections to the Ryu-Takayanagi area formula.
According to the FLM proposal\cite{Faulkner:2013ana} this equals the bulk MI
between the two disjoint regions spanned by the boundary spheres and their
corresponding minimal area surfaces. We compute this quantum correction and
provide in this way a non-trivial check of the FLM proposal.
