The question is quite straightforward, I have some two qubit state and I want to measure it in the Bell basis. This question answers me partly, but I still have some doubts because, I thought that just reversing back the transformation would give me the desired mapping from:
$$ |\Phi^+\rangle \to |00\rangle \\ |\Phi^-\rangle \to |01\rangle \\ |\Psi^+\rangle \to |10\rangle \\ |\Psi^+\rangle \to |11\rangle \\ $$
but it does't seem to work as I thought it would:
By doing the math I understand that it should give this, but what I don't understand is my reasoning to why it is so. That is, why was I wrong thinking that the above circuit would return all the measurements in the $|00\rangle$?