  Quantum Darwinism posits that the emergence of a classical reality relies on
the spreading of classical information from a quantum system to many parts of
its environment. But what are the essential physical principles of quantum
theory that make this mechanism possible? We address this question by
formulating the simplest instance of Darwinism - CNOT-like fan-out interactions
- in a class of probabilistic theories that contain classical and quantum
theory as special cases. We determine necessary and sufficient conditions for
any theory to admit such interactions. We find that every theory with
non-classical features that admits this idealized spreading of classical
information must have both entangled states and entangled measurements.
Furthermore, we show that Spekkens' toy theory admits this form of Darwinism,
and so do all probabilistic theories that satisfy principles like strong
symmetry, or contain a certain type of decoherence processes. Our result
suggests the counter-intuitive general principle that in the presence of local
non-classicality, a classical world can only emerge if this non-classicality
can be "amplified" to a form of entanglement.
