the matter would be needed to be converted into radiation and the
energy required to do so would be determined by E = mc². Since it is
fiction, we assume that the requisite amount of energy is available
and can be target on the object so as to break all the atomic bonds in
a controlled manner. Those atoms could then be sent across in form of
Your understanding is pretty close to the star-trek explanation.
That said, teleportation is improbable for many reasons and an understanding of physics only enforces the improbability. In other words, knowing physics helps you understand why it probably isn't possible more than it tells you how it's possible.
My first concern is that how scientifically correct the above theory
It's unclear if there's a way to gather all a person's quantum information (a huge amount of data - much more than all the computers in the world together). It's not clear that a person could be deconstructed or turned to energy or reconstructed.
And there are problems. If a person is transferred into energy, that's enough energy to vaporize Connecticut. - careful where you point that thing!!
And, pointed out above, is the reassembled person really the same person as the one who went in or just a copy? Do people die every time they are transported and replaced by identical quantum copies with the exact same memories, beliefs and assumptions - so they feel like the same person, they even remember transporting, but are they really the same person? Moral dilemma. McCoy and Barkley were right to be afraid of that thing.
The second concern is that if there is any existing theory which can
be used to justify the reassembly of atoms on the other side to create
the object back?
There's no existing theory that comes close to making transportation possible. The gathering of information, the disassembling and reassembling - all huge (really really huge) speculative jumps. I don't want to say never, but an existing theory that might work - hell no. It's pure fiction at this point.
Some ways to make it perhaps more like real science, but, perhaps less fun is
1) - disable the higgs field. A person's mass can then travel at the speed of light with the Higgs field off, then, reconstruct the higgs field and provided they fly through a well organized tunnel of sorts and not fly in every which direction, maybe you could transport someone that way.
2) - convert them to dark matter, provided dark matter has its own standard model, you could convert and retain the person's energy, cohesion and information while they transform into a ghost-like state, can fly through the ship to somewhere not far away, within a few light seconds, and then be converted back.
3) - open some kind of quantum tunnel or wormhole and they can just jump or step through - yes, it's not as cool, but it avoids the problem if disassembling a person and reassembling them, which is a pretty enormous problem, not to mention, it's possible that it's actually killing the original.
My personal feeling is making transportation less "cool" is the way to go. I like the 3 ideas above though none of them are real science either, but if you want star-trek transportation, enough people have gone with that, the it's no big. It's not science though.