Foundations of Physics 45 (1):62-74 (2015)

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 \ -imperfect cloning operation which tolerates a finite loss \ 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 \ -imperfect cloning operation in the case where the loss of fidelity is less than \ . Therefore in this case no universal \ -imperfect cloning operation is possible in algebraic quantum theory
Keywords No-cloning theorem  Fidelity  Completely positive map   Algebraic quantum field theory
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DOI 10.1007/s10701-014-9843-8
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