Nocloningteoreema

nocloningteoreema is the term used in some languages for the no-cloning theorem in quantum information theory. The theorem states that it is impossible to perfectly copy an arbitrary unknown quantum state. In other words, there is no quantum operation that can take an unknown state and produce two exact copies of that state for every possible input.

Formally, the theorem arises from the linearity of quantum mechanics. If a universal cloning device U existed, it would satisfy U|ψ⟩|0⟩ = |ψ⟩|ψ⟩ for all states |ψ⟩. But considering two different non-orthogonal states and using linearity leads to contradictions, showing that such a universal perfect cloner cannot exist. The result implies that cloning must be approximate or state-dependent if attempted at all.

In practice, only imperfect cloning is possible. Universal quantum cloning machines (UQCM) can produce copies with fidelity below 1. For the simplest case of cloning one qubit into two, the optimal universal fidelity is 5/6 (about 0.833). Variants exist that improve fidelity for specific sets of states, such as phase-covariant cloners, which are tailored to particular input ensembles.

The no-cloning theorem has important consequences for quantum information science and cryptography. It underpins the security of quantum key distribution, since an eavesdropper cannot make perfect copies of unknown quantum states without disturbing them. Numerous experiments have demonstrated approximate cloning and tested its limits in photonic and other quantum systems, reinforcing the theorem’s role as a foundational principle.