Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 10E / c

Projecting the GHZ state onto Charlie's outcome $0$ leaves the unnormalised state $|00{⟩}_{AB}/\sqrt{2}$. After normalization Alice and Bob have $|00⟩$, a product state.

Projecting the three-qubit $W$ state onto Charlie's outcome $0$ leavesAfter normalization this is $(|01⟩+|10⟩)/\sqrt{2}$, a Bell state and hence an entangled state of Alice and Bob.