  We prove a general limitation in quantum information that unifies the
impossibility principles such as no-cloning and no-anticloning. Further, we
show that for an unknown qubit one cannot design a universal Hadamard gate for
creating equal superposition of the original and its complement state.
Surprisingly, we find that Hadamard transformations exist for an unknown qubit
chosen either from the polar or equatorial great circles. Also, we show that
for an unknown qubit one cannot design a universal unitary gate for creating
unequal superpositions of the original and its complement state. We discuss why
it is impossible to design a controlled-NOT gate for two unknown qubits and
discuss the implications of these limitations.
