No-cloning Theorem and Quantum Copying

Heisenberg’s uncertainty relation and Bohr’s principle of complementarity form the foundations of quantum mechanics. If these are violated then the edifice of quantum mechanics can come crashing down. In this chapter, it is shown how cloning or perfect copying of a quantum state can potentially lead to a violation of these sacred principles. A no-cloning theorem is proven showing that the cloning of an arbitrary quantum state is not allowed. The foundation of quantum mechanics is therefore protected. It is also shown how quantum cloning can lead to superluminal communication. It is also discussed that, if making a perfect copy of a quantum state is forbidden, how best a copy of a state can be made.

"PARTIAL" QUANTUM CLONING AND QUANTUM CLONING OF MIXED STATES

We discuss "partial" quantum cloning of pure two-partite states, where only the "part" of the initial state related to one qubit is copied. The same approach gives the possibility of designing a quantum copying machine for mixed qubit states.