One-bit remote preparation of real qubit states (source code)

= One-bit remote preparation of real qubit states
{title2=$iY|\beta_\theta\rangle=|\alpha_\theta\rangle$}

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