= Teleportation with an ambiguous Bell-state phase label
{title2=$\mathcal E(\rho)=\tfrac34\rho+\tfrac14Z\rho Z$}
Suppose a perfect $|\phi^+\rangle$ <Bell pair> is used for <quantum teleportation>, but the sender cannot distinguish the $\phi^+$ and $\phi^-$ <Bell-basis measurement> outcomes and guesses their labels uniformly. Each of the four actual outcomes has <probability> $1/4$. Either ambiguous outcome gives an incorrect <Pauli Z gate> correction with conditional <probability> $1/2$, so the total phase-flip <probability> is $1/4$. The unconditional output is therefore the displayed <phase-flip channel>. For $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$, its <teleportation fidelity> is $\langle\psi|\mathcal E(|\psi\rangle\langle\psi|)|\psi\rangle=1-|\alpha|^2|\beta|^2$. It ranges from $3/4$ on the <Bloch sphere> equator to $1$ at its poles. This averages the output <density operators>, including the ambiguous rounds.
Back to article page
