 Above we suggested that BDMI and SDMI immediately solve the measurement problem. This is right in the case of ideal von Neumann measurements, in which the eigenstates \(\ket{a_i}\) of the measured observable \(A\) of the object system \(S\) become perfectly correlated with the eigenstates \(\ket{p_i}\) of the pointer \(P\) of the measuring apparatus \(M\). However, ideal measurements can never be achieved in practice: the interaction between \(S\) and \(M\) never produces a completely perfect correlation between \(A\) and \(P\). Two kinds of non-ideal measurements are usually distinguished in the literature: