Imperfect Cloning Operations in Algebraic Quantum Theory
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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.
KeywordsNo-cloning theorem Fidelity Completely positive map Algebraic quantum field theory
The author wishes to thank Izumi Ojima and Yutaka Shikano for helpful comments on an earlier draft. The author is supported by the JSPS KAKENHI, No.23701009 and the John Templeton Foundation Grant ID 35771.
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