Pure positive operator-valued measure

A POVM whose nonzero effects have rank one, $E_i=w_i|{\psi }_i⟩⟨{\psi }_i|$, with normalized pure states and $w_i>0$. Completeness is ${\sum }_i{w}_i|{\psi }_i⟩⟨{\psi }_i|=I$. This use of pure concerns effect rank, and does not mean an extremal point in the convex set of all POVMs.