I only said there is a distinct Right circularly polarized state or lR> eigen state and a Left circularly polarized state or lL>. But to conduct an experiment using circular polarizer to find out left/right state is not easy. Measuring the intensity when light pass through is not going to give you the answer, because the intensity is the same (The only difference is phase: zero or 180 degree). in principle: you can set up an interference experiment to check out the phase. But it is not easy to do!)