I have a CS background and am studying quantum computing by myself. Struggling at the moment with the Dirac notation for the teleportation circuit. Here we go:
The circuit starts with the EPR pair between Alice and Bob (qubits entangled):
Then the $CNOT$ is applied (so far so good):
Then the Hadamard (still ok):
But then, the terms are regrouped in order to get the equation below, but I couldn't figure out how that was done.
For instance, I can't figure out how $\beta|1\rangle$ can possibly be multiplying $|00\rangle$ as $\beta$ is only multiplying the terms $|01\rangle$ and $|10\rangle$ part of the equation.
I checked Thomas Wong's book as well as Nielsen and Chuang, but they don't really detail this part at all.