$O :|H \rangle \rightarrow |R \rangle$
$O :|V \rangle \rightarrow |L \rangle$
$O :|L \rangle \rightarrow |H \rangle$
$O :|R \rangle \rightarrow |V \rangle$
where $|R \rangle$, $|L \rangle$ are right circular and left circular light. Is this possible? I should mention that I would also accept the same equations with L,R replaced by linearly polarized light $|D \rangle$, $|A \rangle$. If it is possible, what would be common plates that could do it?