= Two-bit remote state preparation on a graph-state path
Alice holds the first two qubits and Bob the third of a <three-vertex graph-state wire>. Alice measures at $\alpha$ and $(-1)^r\beta$, with outcomes $r,s$, and sends these two bits. Bob applies $Z^rX^s$, the inverse of the known <Pauli frame> $X^sZ^r$, obtaining $U(\beta)U(\alpha)|+\rangle$ up to <global phase>. Bob need not know the angles. Every branch succeeds, with branch probability $1/4$, and no postselection is needed. Alice's measurements and Bob's corrections constitute <local operations and classical communication> on the previously shared entangled resource.
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