  While originally motivated by quantum computation, quantum error correction
(QEC) is currently providing valuable insights into many-body quantum physics
such as topological phases of matter. Furthermore, mounting evidence
originating from holography research (AdS/CFT), indicates that QEC should also
be pertinent for conformal field theories. With this motivation in mind, we
introduce quantum source-channel codes, which combine features of
lossy-compression and approximate quantum error correction, both of which are
predicted in holography. Through a recent construction for approximate recovery
maps, we derive guarantees on its erasure decoding performance from
calculations of an entropic quantity called conditional mutual information. As
an example, we consider Gibbs states of the transverse field Ising model at
criticality and provide evidence that they exhibit non-trivial protection from
local erasure. This gives rise to the first concrete interpretation of a bona
fide conformal field theory as a quantum error correcting code. We argue that
quantum source-channel codes are of independent interest beyond holography.
