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no-cloning theoremtheorem

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The no-cloning theorem was proved in 1982 independently by William Wootters and Wojciech Zurek, and also by Dennis Dieks. It immediately explained why in the quantum world, communication through entanglement does not allow faster-than-light information transfer: the received signal is an unknown state that cannot be copied for repeated verification. The prohibition turned out to be a fundamental limitation born from the linearity of quantum mechanics. Thanks to it, quantum information is fundamentally different from classical information.

How it works

In quantum computers, this means that information is protected from copying: you cannot secretly duplicate data. Quantum cryptography uses this property to create secret keys, and any attempt to intercept them is immediately noticed by the legitimate party as anomalies.

💡 Although perfect cloning is forbidden, one can build 'quantum copying machines' that create imperfect copies with a certain accuracy. They have almost reached the theoretical limit, but will never reach 100%.
\nexists U: U(|\psi\rangle \otimes |e\rangle) = |\psi\rangle \otimes |\psi\rangle \, \forall |\psi\rangle
|ψ⟩ is an arbitrary pure quantum state of the system to be cloned; |e⟩ is a fixed initial state of the auxiliary system (blank slate); U is a unitary evolution operator (deterministic transformation without loss of information); ⊗ is the tensor product (combining two systems into one composite); ∀ is the universal quantifier, emphasizing that cloning must work for any |ψ⟩, which turns out to be impossible.
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Discovered by
Daniel GottesmanDavid DiVincenzoGilles BrassardIgnacio CiracJohn Preskill
Related concepts
quantum error correctionquantum informationquantum key distributionquantum measurementquantum statequantum teleportation
Related laws
Bell's theoremsuperposition principleHeisenberg uncertainty principle

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