Part of the Techucation Quantum Series.
Teleportation is the most over-sold word in quantum computing. It conjures Star Trek transporters and faster-than-light messaging, and almost every popular account quietly implies you end up with a copy of the original. You do not. Quantum teleportation moves an unknown quantum state from one qubit to another while destroying the original, and that destruction is not an incidental detail. It is the mechanism that keeps the protocol on the right side of the no-cloning theorem.
A quick word on no-cloning
This whole protocol is haunted by the no-cloning theorem: there is no operation that copies an arbitrary unknown quantum state. I worked through the proof and its consequences in a recent post, The No-Cloning Theorem in Quantum Computing: Why You Can't Copy a Qubit, so I won't re-derive it here.
The single fact we need: you cannot deterministically duplicate an unknown qubit. The qualifiers matter, because teleportation lives in the gaps between them. The theorem forbids copying unknown states (a known state you can re-prepare at will), it forbids deterministic, perfect copies, and it is a statement about unitary operations — and measurement, which teleportation leans on at the decisive moment, is not unitary.
