 BDMI can be applied directly to the quantum measurement problem. Let us consider an ideal measurement according to the standard von Neumann model, in which a quantum measurement is an interaction between a system \(S\) and a measuring apparatus \(M\). Before the interaction, \(M\) is prepared in a ready-to-measure state \(\ket{p_0}\), eigenvector of the pointer observable \(P\) of \(M\), and the state of \(S\) is a superposition of the eigenstates \(\ket{a_i}\) of an observable \(A\) of \(S\). The interaction introduces a correlation between the eigenstates \(\ket{a_i}\) of \(A\) and the eigenstates \(\ket{p_i}\) of \(P\):