I think this discussion might have already took place here, 
but I will post this to take your opinions on the topic.

How do we define (de)coherence? What makes interference
happen or be lost?

Taking the double-slit experiment in mind, with paths A and B,
the first answer that comes to the mind is that the particle should
not be detected while passing through the slits in a way that we
can tell which path the particle went through.

I like to understand this as if the universes A and B have
changed enough, in the state of a macroscopic number of
particles, in order for us to have access to that information.
So we could postulate that different universes do not interfere.

But is that detection merely the interaction of the particle with
anything? I don't think so. For instance, suppose we use electrons
in a double-path experiment. They take the two paths by
being steered with magnetic fields, and then meet again to interfere
in a screen. I believe this experiment would also produce
interference, but correct me if I'm wrong.

Well, the electrons surely interacted with photons of the
magnetic field, or in last analysis with the electrons that are
producing the magnetic field. Or we could use an arrangement
of electric fields - before anyone argues that 'magnetic fields do
no work' or something - in such a way that the interaction with
some massive particle would be evident. On the other hand,
a photon being deflected by a mirror is also interacting with
something, but still that does not prevent interference from
happening.

If these experiments produce the interference pattern, then the
mere interaction of the particle with anything does not by itself
cause decoherence. What then does? Is it only when a large
enough number of particles change their states? But what would
be the threshold? Or is it the 'information'? But then how do we
define 'information'?

-Eric.

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