Bell measurement on one qubit and one leg of a GHZ state
= Bell measurement on one qubit and one leg of a GHZ state
For $|\alpha\rangle=a|0\rangle+b|1\rangle$, a Bell measurement on $|\alpha\rangle$ and the first leg of a GHZ state leaves the other two legs in $a|00\rangle\pm b|11\rangle$, after applying $X$ to both legs for the two $\Psi$ outcomes.