Superpositions of diffusive superpositions examples?

[James MC]

I take it some common quantum states take the form:

(#|A>1(#|B>2 + #|C>2)) + (#|D>1(#|E>2 + #|F>2))

Here particle 1 is in a superposition of |A> and |D> but is also entangled with particle 2 so that finding 1 to be in |A> will collapse 2 into a |B>/|C> superposition while finding 1 to be in |D> will collapse 2 into a |E>/|F> superposition.

Firstly, are there realistic examples of this (i.e. where it matter for practical purposes) in which 2's wave function spreads?

Here's a fanciful example: an electron gun g that is about to fire an electron is in a superposition of two places (here and there). This would presumably yield:

(#|here>g([e spreads over time])) + (#|there>g([e spreads (slightly differently) over time]))

Is there any realistic examples of quantum states which has this form?

 

[.Scott]

Certainly the answer to your questions are yes.
As far as a realistic example... say a photon (1) is heading towards a double slit, but might first encounter an electron (2) crossing its path. If the photon makes it through the double slit, I believe you would have the kind of situation you're describing here. If we measure the photon at slit A, the electron would have different constraints on it than if we measured the photon at D.

Does that work?