Imperfect cloning operations in algebraic quantum theory

No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal $ε$-imperfect cloning operation which tolerates a finite loss $ε$ of fidelity in the cloned state, and show that an individual system's algebra of observables is Abelian if and only if there is a universal $ε$-imperfect cloning operation in the case where the loss of fidelity is less than 1/4. Therefore, in this case no universal $ε$-imperfect cloning operation is possible in algebraic quantum theory.

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