= Conjugate-state steering from a maximally entangled pair
{title2=$(\langle u|\otimes I)|\Phi_d\rangle=|\overline u\rangle/\sqrt d$}
For $|\Phi_d\rangle=d^{-1/2}\sum_i|ii\rangle$ and normalized $|u\rangle=\sum_i u_i|i\rangle$, contraction of the first factor gives $d^{-1/2}\sum_i\overline{u_i}|i\rangle$. Hence a rank-one <projective measurement> outcome $u$ occurs with <probability> $1/d$ and leaves the other subsystem in the coordinatewise <complex conjugate> state $|\overline u\rangle$. The <complex conjugation> refers to the paired <bases> defining $|\Phi_d\rangle$; it must not be omitted for a complex measurement <vector>. Conditioning is essential: the unconditional <reduced density matrix> remains $I/d$.
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