 Conjugate-state steering from a maximally entangled pair

For $|{\Phi }_d⟩=d^{-1/2}{\sum }_i|ii⟩$ and normalized $|u⟩={\sum }_i{u}_i|i⟩$, contraction of the first factor gives $d^{-1/2}{\sum }_i\overline{u_i}|i⟩$. Hence a rank-one projective measurement outcome $u$ occurs with probability $1/d$ and leaves the other subsystem in the coordinatewise complex conjugate state $|\overline{u}⟩$. The complex conjugation refers to the paired bases defining $|{\Phi }_d⟩$; it must not be omitted for a complex measurement vector. Conditioning is essential: the unconditional reduced density matrix remains $I/d$.