Using their theory of "quantum filters", Farah and Weaver showed that a sufficiently generic filter for the projections in the Calkin algebra produces a pathological pure state. In particular, this generic pure state is not pure when restricted to any atomic maximal abelian self adjoint subalgebra, and is thus a counterexample to a conjecture of Anderson. Using Ramsey-theoretic techniques, we give sufficient conditions for filters of projections to yield counterexample to Anderson's conjecture, and under large cardinal hypotheses, to be generic over the inner model L(R).