Remember: "I think I can safely say that nobody understands quantum mechanics." ~ Richard Feynman Edit: Degenerate means that the measurement doesn't completel

Remember: "I think I can safely say that nobody understands quantum mechanics." ~ Richard Feynman Edit: Degenerate means that the measurement doesn't completely determine the state of the system. In that case the state before the measurement is projected onto the subspace of states compatible with the measurement, I think this may be more or less what you meant by "narrowing down the possibilities".