Impossibility of exact flipping of three arbitrary quantum states via incomparability

We present here a scheme that relates seemingly two different kinds of physical impossibilities of quantum information processing. We derive, exact flipping of three arbitrary states not lying in one great circle is not possible with certainty, by using the existence of incomparable states which are not interconvertible deterministically by local operations and classical communications. In contrast, considering the nonexistence of exact universal flipper, the incomparability of a pair of bipartite pure entangled states can be established.