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So I create the GHZ state already as the photo below $$ |\Delta\rangle=\frac1{\sqrt2}(|000\rangle+|111\rangle) $$ and also I preform a CNOT on the first qubit (as the target qubit), and the second qubit (as the control qubit), $$ \frac1{\sqrt2}(|000\rangle+|111\rangle)=|0\rangle\otimes \frac1{\sqrt2}(|00\rangle+|11\rangle) $$ then after that I have to operate a unitary operation on my third qubit of the GHZ state my only question is do I do with the two separate two independent subsystems or with the qubit that is not longer entangled with the other two, I attached a picture of what the professor did in this part that I'm stuck. $$\sigma_x=\begin{pmatrix}0&1\\1&0\end{pmatrix}$$ $$\lvert \Delta' \rangle = \frac{1}{\sqrt{2}} \left( \lvert 001 \rangle + \lvert 110 \rangle \right)$$ thanks for the help,

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    $\begingroup$ please see quantumcomputing.meta.stackexchange.com/questions/49/… for how to properly render math on the site $\endgroup$
    – glS ♦
    Commented Jul 8 at 17:28
  • $\begingroup$ Not sure whether I understand the question, what you wrote is $\lvert \Delta' \rangle = \mathbb{I} \otimes \mathbb{I} \otimes \sigma_x \lvert \Delta \rangle$. $\endgroup$
    – Refik Mansuroglu
    Commented Jul 9 at 6:09

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