Strongly incompatible quantum devices (Q2015107)

The concept of joint quantum measurability, closely related with that of compatible quantum observables, is expanded to encompass all kinds of possible measurement devices. The notions of incompatibility and next strong incompatibility are introduced for measurement devices. Both incompatibility notions are rigorously characeterized and their difference is demonstrated by examples of measurement models. Technically, the Stinespring representation theorem (and dilation) together with the Kraus decomposition theorem (and operators) are employed. The background for the quantum measurement methodology comes from \textit{T. Heinosaari} and \textit{M. Ziman} [The mathematical language of quantum theory. From uncertainty to entanglement. Cambridge: Cambridge University Press (2012; Zbl 1243.81008)].