Remote preparation in conjugate bases
= Remote preparation in conjugate bases
{title2=$({}_A\langle a|\otimes I_B)|\Phi_+\rangle=|a^*\rangle_B/\sqrt2$}
A <projective measurement> on one half of a <Bell state> prepares the complex-conjugate basis on the other half, conditional on the outcome. Measuring Alice in the columns of $U^*$ prepares Bob in the columns of $U$. Ignoring the equally likely outcomes leaves Bob's <reduced density matrix> equal to $I/2$ in either basis.