= Solution
In <quantum teleportation>, Alice transfers an arbitrary unknown <qubit> $|\chi\rangle=\alpha|0\rangle+\beta|1\rangle$ using one shared <Bell pair> and two bits of <classical communication>. Define $|\beta_{mn}\rangle=(I\otimes X^nZ^m)|\Phi^+\rangle$, with $m,n\in\{0,1\}$. Regrouping the initial three-qubit state into this <Bell basis> gives
$$
|\chi\rangle_1|\Phi^+\rangle_{23}
=\frac12\sum_{m,n}|\beta_{mn}\rangle_{12}X^nZ^m|\chi\rangle_3.
$$
Alice's <Bell-basis measurement> selects each label with <probability> $1/4$. She sends $(m,n)$ to Bob, who applies the inverse $Z^mX^n$, restoring $|\chi\rangle$. The correction depends on the measurement label, not on the unknown amplitudes. Before the message, Bob's average state is $I/2$, independent of the input; <quantum no-signalling> therefore prevents superluminal communication. The shared pair is consumed and Alice does not retain an independent copy, in agreement with the <no-cloning theorem>.
The <Bouwmeester quantum teleportation experiment> used <photon> <polarization>, a down-conversion entangled pair, a beam-splitter Bell-state analyzer and coincidence-conditioned output <polarization> measurements. Temporal indistinguishability of the two analyzer <photons> was essential. Its successful selected Bell outcome demonstrated the state transfer, rather than a deterministic implementation of all four outcomes.<Experimental quantum teleportation by Dik Bouwmeester and others>[1997, experimental realization and Figures 1–5]{ref}
The general experimental tasks are to distribute entanglement, prepare and synchronize the input, perform a sufficiently discriminating joint measurement, communicate the label and apply or account for the correction. A demonstration must test nonorthogonal input states, not merely transfer a known classical basis label. Finite efficiency, accidental coincidences, distinguishability and phase drift reduce success <probability> or <teleportation fidelity>. Postselected verification, a heralded usable output and unconditional deterministic teleportation are distinct experimental claims.
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