  We use holographic methods to characterize the RG flow of quantum information
in a Chern-Simons theory coupled to massive fermions. First, we use
entanglement entropy and mutual information between strips to derive the
dimension of the RG-driving operator and a monotonic c-function. We then
display a scaling regime where, unlike in a CFT, the mutual information between
strips changes non-monotonically with strip width, vanishing in both IR and UV
but rising to a maximum at intermediate scales. The associated information
transitions also contribute to non-monotonicity in the conditional mutual
information which characterizes the independence of neighboring strips after
conditioning on a third. Finally, we construct a measure of extensivity which
tests to what extent information that region A shares with regions B and C is
additive. In general, mutual information is super-extensive in holographic
theories, and we might expect super-extensivity to be maximized in CFTs since
they are scale-free. Surprisingly, our massive theory is more super-extensive
than a CFT in a range of scales near the UV limit, although it is less
super-extensive than a CFT at all lower scales. Our analysis requires the full
ten-dimensional dual gravity background, and the extremal surfaces computing
entanglement entropy explore all of these dimensions.
