Can non-locality be considered an instantaneous propagation of the field? I've read the article Quantum Entanglement, which is a summary of the basics of non-locality, as well a claim for the first "real" proof of its existence. I also have some background from self-studying QFT and reading 
 Matt Strassler's blog.
My question is: is it logical to assume that, if elementary particles are treated as excitations of a underlying field, that non-locality might imply instantaneous propagation "through" the fields?
I appreciate that both the field and the particles should be treated as purely mathematical in nature, but that the particle has more "reality" because we can perform experimental work on it. (And that as far as I want to go regarding any naïve philosophical aspect to physics.)
If we can (mathematically) treat a positron as an electron travelling backwards in time, is it as valid to treat non-locality as an instantaneous propagation in the field? 
 A: Quantum mechanics is based on equations in which no field can travel faster than light. All predictions of quantum mechanics, including quantum entanglement, are therefore in agreement with causality.
A: Both QM and QFT are local. Bell's theorem does not imply non-locality. It implies that any theory that reproduces the predictions of quantum mechanics is non-local if that theory represents the state of a system before a measurement by a stochastic variable, i.e. - a single number that is chosen from a set of possible outcomes with some probability.
There is a local description of the evolution of any given quantum system in terms of its Heisenberg picture observables, which are represented by operators not single numbers. The observables change only when the system changes by itself or through a local interaction with another system.
Entanglement and teleportation can be explained by quantum information being transported locally through decoherent channels. The information is contained in the observables of the channels, but it does not affect their expectation values: locally inaccessible information. This locally inaccessible information can only be unlocked by using it in conjunction with information from the other entangled system:
http://arxiv.org/abs/quant-ph/9906007
http://arxiv.org/abs/1109.6223
This treatment has been extended to quantum field theory too, see
https://arxiv.org/abs/quant-ph/0103079
