No-Cloning Theorem

As we dig deeper into quantum information, quantum cryptography, and quantum computing, we will discover that if we could prepare a qubit in a general quantum state without our knowing what that state is, lots of things in QIS would be much easier. At the same time we would lose much of the utility of qubits and quantum states. The notion of duplicating a general quantum state is called cloning. The formal statement of the impossibility of doing so is called the no-cloning theorem, which we mentioned in the More on State Amplitudes and Probabilities lesson.

First, let’s specify what we would like to accomplish by cloning: we want to prepare a second qubit in (or more accurately, described by) a quantum state that is exactly the same state associated with a previously received qubit.