 An objection raised in this dispute is that a quantity like \(\expval{(\bQ'_{\rm out} - \bQ_{\rm in})^2}^{1/2}\) tells us very little about how good the observable \({\bQ'}_{\rm out}\) can stand in as an inaccurate measurement of \(\bQ_{\rm in}\). The main point to observe here is that these operators generally do not commute, and that measurements of \(\bQ'_{\rm out}\), of \(\bQ_{\rm in}\) and of their difference will require altogether three different measurement contexts. To require that \(\epsilon_\psi(\bQ)\) vanishes, for example, means only that the state prepared belongs to the linear subspace corresponding to the zero eigenvalue of the operator  \(\bQ'_{\rm out} - {\bQ}_{\rm in}\), and therefore that  \(\expval{\bQ'_{\rm out}}_\psi = \expval{\bQ_{\rm in}}_\psi\),  but this does not preclude that the probability distribution of \(\bQ_{\rm out}\) in state \(\psi\) might be wildly different from that of \(\bQ_{\rm in}\). But then no one would think of \(\bQ_{\rm out}\) as an accurate measurement of \(\bQ_{\rm in}\) so that the definition of \(\epsilon_\psi(\bQ)\) does not express what it is supposed to express. A similar objection can also be raised against \(\eta_\psi (\bP)\).