State-dependent implication and equivalence in quantum logic (Q1942174)

The occurrence of an event (represented by a projector \(E\)) leads to a change of a state (represented by a density operator \(\rho\)) into the Lüders state \(E\rho E/[\mathrm{tr}(E\rho)]\). The author shows that two events \(E\) and \(F\) give the same Lüders state iff \(E\rho=F\rho\). The respective classes of equivalence are studied in detail, together with a discussion of a physical interpretation.