Nocloning

Nocloning refers to the no-cloning theorem in quantum information theory, which states that it is impossible to create an exact copy of an arbitrary unknown quantum state. It is a fundamental limit arising from the linearity of quantum mechanics.

Historically, the theorem was proved independently by Wootters and Zurek, and by Dieks in 1982. It shows that no universal cloning machine can replicate all possible quantum states perfectly without disturbing the original state, precluding perfect duplication of unknown quantum information.

Formally, a universal cloning device would take a system in an unknown state |ψ⟩ and an initial blank state to |ψ⟩⊗|ψ⟩. Requiring this to hold for all possible |ψ⟩ leads to contradictions with the preservation of inner products for different input states, except in the trivial case where the states are orthogonal. Consequently, perfect cloning of arbitrary quantum states is impossible.

The theorem has several important implications and nuances. It does not forbid cloning of known states or sets of mutually orthogonal states, and it allows approximate cloning for unknown states, as described by optimal universal quantum cloning machines. State-dependent cloning can be designed for restricted ensembles, achieving higher fidelity within those constraints.

Applications and significance include foundational roles in quantum cryptography, where no-cloning helps ensure the security of quantum key distribution, since eavesdropping cannot be perfectly concealed by cloning. The theorem also influences quantum teleportation and how entanglement is distributed. Experimental work has demonstrated the impossibility of perfect cloning and realized various approximate cloning schemes in photonic systems.