We consider a way to “clone” an arbitrary quantum state. There exists a classical no-go theorem saying that it cannot be possible to clone any arbitrary quantum state without breaking the linearity of quantum mechanics.

A naive idea to “clone”, or to say mass-produce a given state which we know of completely is to prepare a orthonormal basis which contains the desired state as one of its element. Then measure the input state using the aforementioned orthonormal basis will yield the desired sate with a non-zero probability.

However, in order to prepare the orthonormal basis, we need to carry out Gram-Schmidt process on the aforementioned system which has an exponential complexity in the number of qubits. Thus this naive idea fails.