Does this ring a bell for anyone?

Short story set in the future - aliens come to Earth, and bring us the technology they use to travel massive interstellar distances. Nanobots (I think) scan the entire body and brain, then create a physical copy in the far-off place; the original "copy" then dies.

In the story, a woman agrees to be one of the first humans to undergo the process, but something goes wrong. Her copy is created, but her original self doesn't die. This violates the aliens' rule that there can only be one copy of a person in existence, so the guy running the operation is ordered to kill the (original) woman.

This is a convoluted description, but the basic themes of the story were about what constitutes a person's self and soul, and whether a perfect physical copy is, for all intents and purposes, that same person. It was really interesting, and I can't seem to find it anywhere. Does anyone know what it is, and where I might find it?

Thank you!
Rachel