Remote state preparation

Remote state preparation uses a shared entangled state, local quantum measurements and classical communication to prepare a state known to the sender at the receiver. The sender can tailor the measurement to the desired state, so restricted state families can require less communication than quantum teleportation. A real great-circle family of qubit states admits one-bit remote preparation of real qubit states.

For $|{\alpha }_{\theta }⟩=\cos \theta |0⟩+\sin \theta |1⟩$, Alice measures her half of a Bell state in the real basis $\{|{\alpha }_{\theta }⟩,|{\beta }_{\theta }⟩\}$, with $|{\beta }_{\theta }⟩=-\sin \theta |0⟩+\cos \theta |1⟩$. Bob receives one outcome bit and applies $I$ or $iY$. Since $iY|{\beta }_{\theta }⟩=|{\alpha }_{\theta }⟩$ for every $\theta$, the preparation is exact and the correction is independent of the unknown parameter.