No-Cloning Theorem, Leibniz’s Principle, and the Notion of Uniqueness

The impossibility of cloning an unknown quantum state is one of the basic rules governing quantum physics. This statement, known as the “no-cloning theorem”, prohibits perfect cloning, but doesn’t oppose approximate copying. In this paper, we will prove that, due to the uncontrollable quantum fluctuations, no perfect cloning can be achieved. Such a situation allows us to treat the no-cloning theorem as an equivalent one to Leibniz’s principle, and further unify them under the notion of uniqueness; that is, any physical entities (whether macroscopic or microscopic objects) in nature would have its individuality. Moreover, we also demonstrate the universality of unique scheme by showing that, any process of trying to construct one exactly symmetrical or asymmetrical body of a physical object is forbidden. On the whole, nature doesn’t allow the existence of completely identical, symmetrical or asymmetrical things and this conclusion is valid for all physical domains.