  We show that no stabilizer codes over any local dimension can support a
non-trivial area operator for any bipartition of the physical degrees of
freedom even if certain code subalgebras contain non-trivial centers. This
conclusion also extends to more general quantum codes whose logical operators
satisfy certain factorization properties. The results suggest that non-local
"magic" would play an important role in reproducing features of gravitational
back-reaction and the quantum extremal surface formula. We comment on
conditions needed to circumvent the no-go result and provide a simple
prescription for building non-stabilizer codes that do have non-trivial area
operators. We then construct a simple toy example.
