It's more complicated than that (in particular, you need to deal with conservation of information, which is difficult even in a classical particle physics model, and I don't know of any mathematical formalisms that make the quantum case any better), but very approximately yes (in roughly the same sense that, if you cut up a piece of cheese into smaller and smaller pieces, you eventually end up with a single cheese atom).

For example, if a photon decays (spontaneous pair production) into a electron and a positron, those two particles will have some of their information content 'entangled', and that is roughly the same information that would be 'preserved' accross a electron (say, in a atom) emitting a photon to drop into a lower energy level. Because those are the same particle interaction, rotated into different reference frames. (In practice, I think you mostly end up with entanglements like Bit_γ xor Bit_e xor Bit_e̅ = 0, which is why a electron and positron (or matter and antimatter in general) can always annihilate to form a photon (respectively photons) in yet another rotation of said particle interaction.)