Imperfect Cloning Operations in Algebraic Quantum Theory
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- Kitajima, Y. Found Phys (2015) 45: 62. doi:10.1007/s10701-014-9843-8
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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.