Unified Quantum No-Go Theorems of Pure States

Various results of the no-cloning theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. We prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes various no-go theorems of the no-cloning theorem, no-anticloning theorem, no-splitting theorem as a special case.