# What is the difference between having a single-qubit state and knowing a result of a measurement you want to perform on it?

In the quantum teleportation protocol Alice can send Bob an unknown quantum state $$|\psi\rangle$$. If the only thing Bob does with $$|\psi\rangle$$ is to measure it in some basis, I guess it would be simpler for Alice to just do the measurement herself and send the result to Bob. That would not require a shared entangled pair but Alice would need to know Bob's favorite basis. Is there something Bob can do with an actual state $$|\psi\rangle$$ which can not be done with information that Alice sends to Bob?

More generally, due to Holevo bound only a single bit of information can be encoded in a qubit. What is then the difference between teleporting an actual quantum state $$|\psi\rangle$$ and sending the result of some measurement of this state?

• aren't you essentially asking what added advantages does sharing an entangled state has compared to just sharing classically correlated states?
– glS
Sep 17, 2021 at 10:46