User:Donaldfee/sandbox

Quantum cloning is a process that takes an arbitrary, unknown quantum state and makes an exact copy without altering the original state in any way. Quantum cloning is forbidden by the laws of quantum mechanics as shown by the no cloning theorem, which states that there is no operation for cloning any arbitrary state $${\displaystyle |\psi \rangle _{A}} $$ perfectly. In Dirac notation, the process of quantum cloning is described by:

$${\displaystyle U|\psi \rangle _{A}|e\rangle _{B}=|\psi \rangle _{A}|\psi \rangle _{B}},$$

where $${\displaystyle U} $$ is the actual cloning operation, $${\displaystyle |\psi \rangle _{A}} $$is the state to be cloned, and $${\displaystyle |e\rangle _{B}}$$ is the initial state of the copy.

Though perfect quantum cloning is not possible, it is possible to perform imperfect cloning, where the copies have a non-unit (i.e. non-perfect) fidelity. The possibility of approximate quantum computing was first addressed by Buzek and Hillery, and theoretical bounds were derived on the fidelity of cloned quantum states

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One of the applications of quantum cloning is to analyse the security of quantum key distribution protocols. Teleportation, nuclear magnetic resonance, quantum amplification, and superior phase conjugation are examples of some methods utilized to realize a quantum cloning machine. Ion trapping techniques have been applied to cloning quantum states of ions.