My take on the star trek transporter:
It breaks you up into billions of pieces, effectively killing you. It reassembles an exact copy that, if it is alive, has no human soul and no intelligence.
But you are still dead.
Increasing the distance between your atoms is not equivalent to killing you. Such an increase happens whenever you take a deep breath.
One could say that the totality of those atoms will cease to function as a biological, sentient computer. But this also happens every night, when our bodies switch into mental regeneration mode and are no longer under our control. Is a sleeping man alive? If yes, he is just as alive as grass.
By the way, one of ST:TNG episodes is entirely built around the idea that humans retain consciousness while in transport.
It reassembles an exact copy that, if it is alive, has no human soul and no intelligence.
If the copy is exact then nothing will be lost. If something is lost then the copy is not exact.
As matter of fact, most cells that human bodies are built with do not live forever. They have very short lifespan after which they are replaced with their copies.
In this aspect it is interesting that in ST:TNG transporters are used for transportation, but never for medical purposes. It would be very attractive to make changes in the pattern buffer before reconstituting the person. This would allow to heal *anything* in a second. ST:TNG stories carefully steer around long term storage of human patterns, but the issue did arise in a couple of episodes. It may be that the pattern is of holographic nature, where every bit is affected by all atoms and affects all atoms of the object - so it is computationally difficult to make targeted modifications.
Look up the story "Think Like a Dinosaur" -- it covers this exact topic (minus any reference to Star Trek).
My take on the star trek transporter:
It breaks you up into billions of pieces, effectively killing you. It reassembles an exact copy that, if it is alive, has no human soul and no intelligence.
This explain Captain Janeway, No Soul!