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Emile comments on Open thread, August 5-11, 2013 - Less Wrong Discussion
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(Warning: I am not a physicist; I learnt a bit of about QM from my physics classes, the Sequences, Feynmann Lectures on Physics, and Good and Real, but I don't claim to even understand all that's in there)
I'm not sure I totally understand your question, but I'll take a stab at answering:
The important thing is configuration space, and spatial distance is just one part of that; there is just one configuration space over which the quantum wave-function is defined, and points in configuration space correspond to "universe states" (the position, spin, etc. of all particles).
So two points in configuration space A and B "interfere" if they are similar enough that both can "evolve" into state C, i.e. state C's amplitude will be function of A and B's amplitudes. The more different A and B are, the less likely they are to have shared "descendant states" (or more precisely, descendant states of non-infinitesimal amplitude), so the more they can be treated like "parallel branches of the universe". Differences between A and B can be in psychical distance of particles, but also of polarity/spin, etc. - as long as the distance is significant on one axis (say spin of a single particle), physical distance shouldn't matter.
I think spin could be an example of "another axis" you're looking for (though even thinking in terms of Axis may be a bit misleading, since all the attributes aren't nice and orthogonal like positions in cartesian space).
This is pretty much correct, but to be more general and not just restrict yourself to the position basis, you can talk about the wavefunction in general, in terms of the eigenvector basis.
Two states 'strongly interact' if they share many of their high-amplitude eigenvectors. This is because eigenvectors evolve independently, and so if you have two states that do not share many eigenvectors, they will also evolve independently.
In the position basis, this winds up being much the same as having particles far from each other. In the momentum basis, it's less intuitive. You can have states with very similar representations in this basis but nevertheless very different eigenvector expansions.
I must admit I have very little understanding of how eigenvectors fit in with QM. I'll have to read up more on that, thanks for pointing out holes in my knowledge (though in the domain of QM, there are a lot of holes).