I saw the concept of quantum teleportation, and they say you have a pre-shared state between alice and bob, such as Alpha|1>+Beta|0>, with Alpha=Beta=1/sqrt(2). Then you apply a little circuit with a couple of CNOTs and Hs, then do a measurement which gives you two classical bits as a result. And then you send the two classical bits, and then bob recovers the state according to those two classical bits and the pre-shared state. However, I don't see how this would work when the state to transmit has, for example, Alpha=sqrt(0.1345) and Beta=sqrt(0.8655), because, you can actually get different measurements repeating the same experiment, and I dont see how you would get the example numbers from a maximally entangled state and two classical bits, seems impossible.

Probably I am missunderstanding the purpose of quantum teleportation or missing something big. Thanks for any help.

I saw the concept of quantum teleportation, and they say you have a pre-shared state between Alice and Bob, such as $\alpha\vert 1\rangle+\beta\vert 0\rangle$, with $\alpha=\beta=\frac{1}{\sqrt{2}}$. Then you apply a little circuit with a couple of CNOTs and Hs, then do a measurement which gives you two classical bits as a result. And then you send the two classical bits, and then bob recovers the state according to those two classical bits and the pre-shared state. However, I don't see how this would work when the state to transmit has, for example, $\alpha=\sqrt{0.1345}$ and $\beta=\sqrt{0.8655}$, because, you can actually get different measurements repeating the same experiment, and I don't see how you would get the example numbers from a maximally entangled state and two classical bits, seems impossible.

Probably I am misunderstanding the purpose of quantum teleportation or missing something big. Thanks for any help.