Survey: No-Cloning Theorem

The no-cloning theorem has always been a hot topic in quantum theorem: As an impossibility result, this theorem precludes attempts to communicated faster than light and reinforces the security of several quantum cryptography protocol. In this survey, I will briefly introduce the history of quantum no-cloning theorem–how the thesis was invented, how did it get its name; And i would also discuss the hitherto progress on no-cloning theorem, several approach of none-perfect cloning on non-orthogonal states as well as the application of quantum no-cloning theorem in quantum cryptography and quantum information. This survey incorporates the lecture ”Quantum Information Amplifiers Beyond the No-Cloning Theorem” given by Prof. Giulio Chiribella and ”Quantum cryptography” given by Prof. Xiongfeng Ma.