No-cloning theorem in Quantum Computing
In classical computing systems, it is taken for granted that digital data can be copied with perfect accuracy. The no-cloning theorem describes one of the most fundamental properties of quantum systems, namely, there is no unitary operation that will perfectly copy an arbitrary quantum state.
An arbitrary state in this context means any state of a specified Hilbert space that is being considered. This limits the available resources for programming a quantum computer. However, the no-cloning feature is extremely important in quantum cryptography because the inability of copying an unknown quantum state is a contributing factor to the system’s security.
Theorem: There is no valid quantum operation that maps an arbitrary state | Ψ> to |Ψ> |Ψ>