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.
Cite this paper
Yao, Q. , Zhang, B. , Luo, Y. and Huang, H. (2014). No-Cloning Theorem, Leibniz’s Principle, and the Notion of Uniqueness. Open Access Library Journal, 1, e981. doi: http://dx.doi.org/10.4236/oalib.1100981.
Fuchs, C.A. and Peres, A. (1996) Quantum-State Disturbance versus Information Gain: Uncertainty Relations for Quantum Information. Physical Review A, 53, 2038-2045.