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arXiv:1010.6103

Cloning in Classical Mechanics

Aaron Fenyes

Published Oct 28, 2010• 1 citation
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Abstract

In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, more inclusive definition of cloning, we give examples of classical cloning processes. We also prove that a cloning machine must be at least as complicated as the object it is supposed to clone.

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In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, more inclusive definition of cloning, we give examples of classical cloning processes. We also prove that a cloning machine must be at least as complicated as the object it is supposed to clone.

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The quantum no cloning theorem is an essential result in quantum information theory. Following this idea, we give a physically natural definition of cloning in the context of classical mechanics using symplectic geometry, building on work of A. Fenyes, J. Math. Phys. 53, 012902 (2012). We observe, following Fenyes, any system with phase space (R2N,dxi∧dyi) can be cloned in our definition. However, we show that if (M, ω) can be cloned in our definition, then M must be contractible. For instance, this shows the simple pendulum cannot be cloned in Hamiltonian mechanics. We further formulate a robust notion of approximate cloning, and show that if (M, ω) can be approximately cloned, then M is contractible. We give interpretations of our results and in some special cases reconcile our no cloning theorems with the general experience that classical information is clonable. Finally we point to new directions of research, including a connection of our result with the classical measurement problem.

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The paper queries correctness of quantum no-cloning theorem that is very imporant in the quantum information technology and the whole quantum mechanics.The proof of quantum no-cloning theorem is very simple and it can’t exclude all kinds of possible cloning.Some parts of the proof are doubtful and not very clearly proved.While quantum mechanics is very complex and not completely known,the principle of complementarity shows that it is incorrect to explain everything in a simple way.The development of science tells us many things such as measurement and copy of a particle that are thought to be impossible in a stage,may be possible when the more profound,precise and tiny characteristics is found out.If it is possible to measure in an indirect way that can’t change the measured quantum state,the quantum cloning is possible.The wave-particle duality and uncertainty relation in quantum mechanics are very hard to imagine,but they are very similar to the phenomenon of the society and human in which copy and cloning is possible.If the quantum state has something like gene,it is possible to cloning a quantum state.

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Minghao Wang, Qing-Yu Cai

The correspondence principle suggests that a quantum description for the microworld should be naturally transited to a classical description within the classical limit. However, it seems that there is a large gap between quantum no-cloning and classical duplication. In this paper, we prove that a classical duplication process can be realized using a universal quantum cloning machine. In the classical world, information is encoded in a large number of quantum states instead of one quantum state. When tolerable errors occur in a small number of the quantum states, the fidelity of duplicated copies of classical information can approach unity. That is, classical information duplication is equivalent to a redundant quantum cloning process with self-correcting.

arXiv:1803.05602•Mar 15, 2018•2 citations
In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, more inclusive definition of cloning, we give examples of classical cloning processes. We also prove that a cloning machine must be at least as complicated as the object it is supposed to clone.
The quantum no cloning theorem is an essential result in quantum information theory. Following this idea, we give a physically natural definition of cloning in the context of classical mechanics using symplectic geometry, building on work of A. Fenyes, J. Math. Phys. 53, 012902 (2012). We observe, following Fenyes, any system with phase space (R2N,dxi∧dyi) can be cloned in our definition. However, we show that if (M, ω) can be cloned in our definition, then M must be contractible. For instance, this shows the simple pendulum cannot be cloned in Hamiltonian mechanics. We further formulate a robust notion of approximate cloning, and show that if (M, ω) can be approximately cloned, then M is contractible. We give interpretations of our results and in some special cases reconcile our no cloning theorems with the general experience that classical information is clonable. Finally we point to new directions of research, including a connection of our result with the classical measurement problem.
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.
The paper queries correctness of quantum no-cloning theorem that is very imporant in the quantum information technology and the whole quantum mechanics.The proof of quantum no-cloning theorem is very simple and it can’t exclude all kinds of possible cloning.Some parts of the proof are doubtful and not very clearly proved.While quantum mechanics is very complex and not completely known,the principle of complementarity shows that it is incorrect to explain everything in a simple way.The development of science tells us many things such as measurement and copy of a particle that are thought to be impossible in a stage,may be possible when the more profound,precise and tiny characteristics is found out.If it is possible to measure in an indirect way that can’t change the measured quantum state,the quantum cloning is possible.The wave-particle duality and uncertainty relation in quantum mechanics are very hard to imagine,but they are very similar to the phenomenon of the society and human in which copy and cloning is possible.If the quantum state has something like gene,it is possible to cloning a quantum state.
The correspondence principle suggests that a quantum description for the microworld should be naturally transited to a classical description within the classical limit. However, it seems that there is a large gap between quantum no-cloning and classical duplication. In this paper, we prove that a classical duplication process can be realized using a universal quantum cloning machine. In the classical world, information is encoded in a large number of quantum states instead of one quantum state. When tolerable errors occur in a small number of the quantum states, the fidelity of duplicated copies of classical information can approach unity. That is, classical information duplication is equivalent to a redundant quantum cloning process with self-correcting.