Impossible and Possible Operations in Quantum Information
Arun Kumar Pati · arXiv (Cornell University) · 2001
We prove a general limitation in quantum information that unifies the no-cloning and no-complementing principles. We show that one cannot design Hadamard and unitary gates for creating equal and unequal superpositions of the original and its complement state. We show that if an unknown qubit is chosen from polar great circle then it is possible to design above logic gates. But qubits chosen from equatorial great circle cannot be. We also discuss why one cannot design a controlled-NOT gate for unknown qubits. An important implication of these limitations is that ultimate quantum computers will be inherently personal.