(This was a homework question, the professor gave the answer but not the actual work to get there, as it's considered very easy and purely 'work', but I can't figure it out.)
Alice shares a $|\Phi^+\rangle$ with Bob and another one with Charlie. What happens if Alice does a bell measurement on her two qubits? More precisely, in which entangled states is the pair of qubits owned by Bob and Charlie, in regards to Alice's result?
So basically, after creating the two $|\Phi^+\rangle$ states, Alice does a CNOT on her qubits followed by a Hadamard on the first and then measurement on both.
I know Bob and Charlie now are entangled in a Bell states, and I assume they get a $|\Phi^+\rangle$ if Alice measured 0 and 0, and a $|\Psi^+\rangle$ if she measured 0 and 1, a $|\Psi^-\rangle$ for 1 and 0, and finally a $|\Phi^-\rangle$ for 1 and 1.
My problem is : if she measures 0 and 0, doesn't that collapse the system into a simple $|00\rangle$ for Bob and Charlie? The math of the Bell measurement on Alice's qubits confuses me. How can I do a CNOT on her two qubits since they are entangled with Bob and Charlie? Hopefully I'm clear enough, this is my first question and my quantum knowledge (and latex) is sadly quite limited.
Thank you for any hints! I definitely do not need the actual states they end up with, as I simply want to know how to do the work to get there :)