I think dreams illustrate the human brain's remarkable ability to 3D render detailed fictional events, which explains a lot of the crazy stuff people have believed throughout history.
Trying to explain everyday experience using quantum mechanics usually leads to pseudoscientific hogwash.
I would not be so quick to say, with such certainty, that I know to what degree any organism can experience the division of universes.
I believe I've died many times in many timelines and wake up each day in one I'm still alive in... sometimes with fading memories of the one I just left. (Obviously, there's no way to prove or disprove this, so I normally don't trouble to tell people; they'll either find it out for themselves or I'm wrong, just a broken set of neurons seeking some higher order in its own chaos).
Why would the universe be more likely to send me memories from one of my distant branches, than from another currently-living person? I don't think telepathy exists in either case.
No information has to be transfered in these cross-universe death/wake-ups. You can simply wake up with no recollection of the dream.
I'm not suggesting that branches containing separate information ever merge. I think my language was imprecise. I'm suggesting that one's perception of self-awareness and consciousness merges. The consciousness you have access to leaps to the next available branch.
[edit] I'm not on any meds, never taken antidepressants, and I've never done psychedelics. I do smoke pot occasionally, but oddly it tamps down the intensity of the dreams; the most vivid or memorable ones occur when I'm completely sober.
To be honest, I don't think my dreams are more vivid than other people's; I just think I remember them better because I focus on trying to save them when I wake up. My father and brother both claim they never dream, but once in awhile they've remembered bits of one and they sound as wild as mine.
I don't mind nightmares. I kind of like them. Even if they're horrific I end up recalling them to help myself get back to sleep; then usually the ending changes.
I've never tried to lucid dream, but I'm afraid that if I could control them my dreams would lose the thing that makes them so valuable to me, which is that from their strangeness and randomness, I get to interpret what my other selves are trying to tell me. If my conscious mind controlled them, I think I would lose insight into that; I even wonder whether losing those voices and other lives in my sleep would be a step toward going insane in waking life.