  We establish the non-existence of a universal Hadamard gate for arbitrary
unknown qubits, by considering two different principles; namely,
no-superluminal signalling and non-increase of entanglement under LOCC. It is
also shown that these principles are not violated if and only if the qubit
states are of a special form obtained in our recent work [ IJQI (in press),
quant-ph/0505068 ].
