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 $\epsilon$-imperfect cloning operation which tolerates a finite loss $\epsilon$ 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 $\epsilon$-imperfect cloning operation in the case where the loss of fidelity is less than 1/4. Therefore, in this case no universal $\epsilon$-imperfect cloning operation is possible in algebraic quantum theory.