No-Flipping as a consequence of No-Signalling and Non-increase of   Entanglement under LOCC
  Non existence of Universal NOT gate for arbitrary quantum mechanical states is a fundamental constraint on the allowed operations performed on physical systems. The largest set of states that can be flipped by using a single NOT gate is the set of states lying on a great circle of the Bloch-sphere. In this paper, we show the impossibility of universal exact-flipping operation, first by using the fact that no faster than light communication is possible and then by using the principle of "non-increase of entanglement under LOCC". Interestingly, exact flipping of the states of any great circle does not violate these two principles, as expected. 
Indrani Chattopadhyay, Sujit K. Choudhary, Guruprasad Kar, Samir   Kunkri, Debasis Sarkar