As an identical twin let me chime in here.
Erm... no we don't...
Same originating DNA but
probably material divergence in methylation.
What's interesting between us is that there have always been marginal differences between us whilst growing up; I'm a cm taller, have facial contour differences, I'm left-handed and he's right-handed etc.
From birth there were also strange and distinctive differences such as our fingerprints being identical but opposite (i.e. prints on my left hand are the same as those on his right etc).
We've never experienced the fabled cognitive twin neural link that people talk about, however I know a few female identical twins who claim to share some kind of connection (empathic in nature as far as it's been described -> think Sense8 without the telepathic communication) so I do wonder whether there's a gender bias to that, assuming it is a real thing.
We have had a lot of coincidental thought when we were much younger but I think much of that was a product of nurture being the shared life & environment we grew up in. After we split living together when we left home for Uni we've become so different as people (different career paths, relationships, environments & life experiences) that that hasn't really happened since.
Do I think there is some quantum link between us? Nah...
Do I believe we're two separate consciousnesses? Of course.
Do I believe that consciousness is defined by and rooted in some as-yet-to-be-understood quantum mechanics/phenomena? Absolutely!
Ya'll should check out Sir Roger Penrose's book
The Emperor's New Mind (1989) which theorizes that consciousness is
not algorithmic and thus, much of what we understand about the physical mechanisms of the human brain, whilst still governing a complex mesh of biological and physical functions, do not yet demonstrate the ability to drive or orchestrate what we understand as consciousness in the philosophical sense, and that there is something else going on, perhaps at the quantum level but through phenomena we have yet to either observe, intuit or hypothesize mathematically.
So what does that mean for teleportation? Well it's unclear, but depending on the nature of consciousness, without that base understanding, it's not even 100% clear that even if you can perfectly reconstruct the atomic structure you're actually going to be replicating the consciousness too as a by-product.
In some ways I would personally go so far as to contemplate that it would be impossible to do that, considering the
Heisenberg Uncertainty principle, surely it would be
impossible to even perfectly replicate every attribute (position, velocity, spin) of every particle of every atom, of every molecule, of every protein of every cell in the human body. Imperfect replication maybe possible but then whilst it may guarantee parity across molecular structures, it certainly won't guarantee anything else beyond that so you never have any chance of seeing a "perfect" copy come out the other end.