Discrimination between states of a quantum system by observations
As the author points out, all mathematical problems from this paper are motivated by quantum statistical considerations. Let \(\mathcal M\) be a von Neumann algebra, and let \(\alpha_ i: {\mathcal A}_ i\to {\mathcal M}\) be a net of positive unital mappings, where \(A_ i\) is a finite-dimensional algebra. The existence of a net \(\beta_ i: M\to A_ i\) such that \(\omega\circ \alpha_ i\circ \beta_ i\to \omega\) and \(\varphi\circ \alpha_ i\circ \beta_ i\to \varphi\) is studied, where \(\omega\) and \(\varphi\) are two given normal states. The author finds a necessary and sufficient condition for the existence of \(\beta_ i\), and observes that this condition may fail when \(A_ i\) are commutative but \(\omega\) does not commute with \(\varphi\). When \({\mathcal M}\), \(\omega\), \(\varphi\), are infinite tensor products, the author gives a reformulation in terms of relative entropy.
scientific article; zbMATH DE number 599750