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 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.
Heisenberg’s uncertainty relation and Bohr’s principle of complementarity form the foundations of quantum mechanics. If these are violated then the edifice of quantum mechanics can come crashing down. In this chapter, it is shown how cloning or perfect copying of a quantum state can potentially lead to a violation of these sacred principles. A no-cloning theorem is proven showing that the cloning of an arbitrary quantum state is not allowed. The foundation of quantum mechanics is therefore protected. It is also shown how quantum cloning can lead to superluminal communication. It is also discussed that, if making a perfect copy of a quantum state is forbidden, how best a copy of a state can be made.
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 celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Found. Phys. 1, 23–33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park's demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning.
A fundamental question in quantum mechanics is, whether it is possible to replicate an arbitrary unknown quantum state. Then famous quantum no-cloning theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open the following question: If the state is not arbitrary, but secretly chosen from a certain set $$={ | Ψ_1> ,| Ψ_2> ,... ,| Ψ_n> } $, whether is the cloning possible? This question is of great practical significance because of its applications in quantum information theory. If the states ∣Ψ1>,∣Ψ2>,... and $| Ψ_n> $ are linearly-dependent, similar to the proof of the no-cloning theorem, the linearity of quantum mechanics forbids such replication. In this paper, we show that, if the states ∣Ψ1>,∣Ψ2>,... and $| Ψ_n> $ are linearly-independent, they do can be cloned by a unitary-reduction process.
The no-cloning theorem is a basic limitative result for quantum mechanics, with particular significance for quantum information. It says that there is no unitary operation that makes perfect copies of an unknown (pure) quantum state. We re-examine this foundational result from the perspective of the categorical formulation of quantum mechanics recently introduced by the author and Bob Coecke. We formulate and prove a novel version of the result, as an incompatibility between having a “natural” copying operation and the structural features required for modeling quantum entanglement coexisting in the same category. This formulation is strikingly similar to a well-known limitative result in categorical logic, Joyal's lemma, which shows that a “Boolean cartesian closed category” trivializes and hence provides a major roadblock to the computational interpretation of classical logic. This shows a heretofore unsuspected connection between limitative results in proof theory and no-go theorems in quantum mechanics. The argument is of a robust, topological character and uses the graphical calculus for monoidal categories to advantage. 1.1 Introduction The no-cloning theorem (Dieks 1982; Wootters and Zurek 1982) is a basic limitative result for quantum mechanics, with particular significance for quantum information. It says that there is no unitary operation that makes perfect copies of an unknown (pure) quantum state. A stronger form of this result is the no-broadcasting theorem (Barnum et al. 1996), which applies to mixed states. There is also a no-deleting theorem (Pati and Braunstein 2000).
Quantum information theory is a wide area of investigation, which includes two main subjects: quantum computation and quantum communication. The success of quantum computation theory is due to a positive result: Shor's algorithm. The algorithm provides factorization of integers in a much more efficient way with respect to what is achieved not only by present-day computers, but even by the most powerful conceivable computers based on classical physics. On the other hand, the success of quantum communication is due to the intrinsic security of ideal quantum cryptographic protocols, and thus relies on a negative result, that is the impossibility of reading quantum information without scrambling it in an unrecoverable way. The no information without disturbance property spawns other no-go theorems, which represent some of the most famous and classic results in quantum information theory. Among these results one can certainly list the no-cloning theorem, stating the impossibility of copying quantum information. This impossibility is clearly a consequence of the impossibility of extracting information without disturbing it. Indeed, if we could copy exactly the state of a system, reproducing it on another system of the same type, then we would also be able to iterate this process, and produce as many copies as we want. We could then extract all the information we are interested in from the copies, keeping the original intact. This argument is so simple, but hides a very deep point about quantum information, and more generally about any type of information that can be purified. Suppose indeed that there exists a measurement allowing us to determine the state of a system, with absolute precision. We could then use such a measurement on the system, and once we know its exact state, we can in principle re-prepare the same state as many times as we want. If copying the state is forbidden within a theory, we must then conclude that, in that theory, measuring the state is forbidden, too! This is exactly the case in theories with purification, and in particular in quantum theory. In quantum theory, determining the state of a system is impossible. We can only have some information about what state our system is prepared in. The information may be accurate, but it will never be certain. This could be practically the case in classical theory, too.