Canonical phase measurement is pure
Teiko Heinosaari, Juha-Pekka Pellonpää · Physical Review A · 2009
We show that the canonical phase measurement is pure in the sense that the corresponding positive operator valued measure (POVM) is extremal in the convex set of all POVMs. This means that the canonical phase measurement cannot be interpreted as a noisy measurement even if it is not a projection valued measure.