= Localizing a Bell pair from a GHZ state
{title2=$|\mathrm{GHZ}\rangle_{ABC}\longrightarrow|\Psi^+\rangle_{AB}$}
Charlie measures his qubit of a <GHZ state> in the $X$ basis. The two equally likely outcomes leave Alice and Bob in the <Bell states> $\Phi^+$ or $\Phi^-$, respectively. Charlie sends the outcome bit $c$ to Bob, who applies the <Pauli operator> $XZ^c$, giving $\Psi^+$ in either case. This is deterministic <LOCC> entanglement localization. If Charlie's record is ignored, Alice and Bob instead have the separable mixture $(|00\rangle\langle00|+|11\rangle\langle11|)/2$. The classical outcome is necessary to turn the conditional entanglement into a known usable Bell pair.
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