I saw that mathematica already had other quantum computer questions here, so I think this is the best stack-exchange to ask it.
Lets say you have two qubits. The first is hadamard transformed and the second is a 0.
When you then do a $CNOT$ transform, you get:
$\begin{bmatrix}1&0&0&0\\ 0&1&0&0\\ 0&0&0&1\\ 0&0&1&0 \end{bmatrix} \begin{bmatrix}\sqrt{\frac 1 2}\\ 0\\ \sqrt{\frac 1 2}\\ 0 \end{bmatrix} = \begin{bmatrix}\sqrt{\frac 1 2}\\ 0\\ 0\\ \sqrt{\frac 1 2} \end{bmatrix} $
Note that the order in the vector from top to bottom is $|00\rangle, |01\rangle, |10\rangle, |11\rangle$
You can clearly see now that both qubits are entangled, since the outcome is either $|00\rangle$ or $|11\rangle$ when reading either qubit and either has a 50% chance to be the outcome.
My question is this: if you now apply a hadamard transform to the second qubit, what would happen to the state of the two qubits? How would you perform such a transformation on entangled qubits?